crsi-design guide for economical reinforced concrete

Concrete ReinforcingSteel Institute

Design Guide for

Economical Reinforced

Concrete Structures

2016

A guide to assist design professionals in achieving overall economy in the

design and detailing of reinforced concrete structures.

First Edition

https://telegram.me/seismicisolation

Founded in 1924, the Concrete Reinforcing Steel Institute (CRSI) is a technical institute and an ANSI-accredited Standards Developing Organization (SDO) that stands as the authoritative resource for information related to steel reinforced concrete construction. Serving the needs of engineers, architects and construction professionals, CRSI offers many industry-trusted technical publications, standards documents, design aids, reference materials and educational opportunities. CRSI Industry members include manufacturers, fabricators, material suppliers and placers of steel reinforcing bars and related products. Our Professional members are involved in the research, design, and construction of steel reinforced concrete. CRSI also has a broad Region Manager network that supports both members and industry professionals and creates awareness among the design/construction community through outreach activities. Together, they form a complete network of industry information and support.


Publicaton No: 10-DG-STRUCTURES

ISBN: 978-1-943961-20-7

Copyright © 2016

By Concrete Reinforcing Steel Institute

First Edition Printed 2016

All rights reserved. This guide or any part thereof may not be reproduced in any form without the written permission of the Concrete Reinforcing Steel Institue.

Printed in the U.S.A

This publication is intended for the use of professionals competent to evaluate the significance and limitations of its contents and who will accept responsibility for the application of the material it contains. The Concrete Reinforcing Steel Institute reports the foregoing material as a matter of information and, therefore, disclaims any and all responsibility for application of the stated principles or for the accuracy of the sources other than material developed by the Institute.

iConcrete Reinforcing Steel Institute

Design Guide for Economical Reinforced Concrete Structures


David A. Fanella, Ph.D., S.E., P.E., F.ASCE, F.ACI is the Senior Director of Engineering at the Concrete Reinforcing Steel Institute. He has over 25 years of experience in the design of a wide variety of low-, mid-, and high-rise buildings and other structures. Fanella has authored numerous technical publications and recently authored a textbook on reinforced concrete design for McGraw Hill. He is a member of ACI Committees 314, Simplified Design of Concrete Buildings; 374, Performance-Based Seismic Design of Concrete Buildings; 375, Performance-Based Design of Concrete Buildings for Wind Loads; and SA04, Design Award. Fanella is a Fellow of the Ameri-can Concrete Institute (ACI) and the American Society of Civil Engineers (ASCE). He also serves as an Associate Member of ASCE Committee 7, Minimum Design Loads for Buildings and Other Structures. He received his BS, MS, and PhD in structural engineering from the University of Illinois at Chicago, Chicago, IL. He is a licensed structural and professional engineer in Illinois and is a licensed professional engineer in many other states.

Author

The following figures and tables courtesy of Reinforced Concrete Structures: Analysis and Design, Second Edition by David Fanella. ©2015, McGraw-Hill Education:

Figures 3.2, 4.1, 4.2, 4.3, 4.4, 4.5, 4.8, 4.9, 4.11, 4.12, 5.6, 5.24, 5.25, 5.26, 5.27, 5.28, 5.29, 5.30, 5.31, 5.32, 6.1, 6.2, 6.3, 6.11, 6.12, 6.13, 6.14, 6.15, 6.16, 7.22, 7.23, 7.24, 8.1, 8.2, 9.1, 9.2, 9.15, 9.16, 9.17, and 9.18

Tables 6.1 and 6.2

ii Concrete Reinforcing Steel Institute



ContentsAuthor ii

Chapter 1Introduction 1-1

1.1 Overview 1-1

2.2 Scope 1-1

Chapter 2Economical Reinforced Concrete

Floor Systems 2-1

2.1 Overview 2-1

2.2 General Guidelines for Economical Reinforced 2-1 Concrete Floor Systems

2.2.1 Overview 2-1

2.2.2 Formwork 2-1

2.2.3 Reinforcement 2-2

2.2.4 Concrete 2-4

2.3 Selecting an Economical Reinforced 2-5 Concrete Floor System

2.3.1 Overview 2-5

2.3.2 One-way Joist System 2-5

2.3.3 Flat Plate System 2-8

2.3.4 Flat Slab System 2-9

2.3.5 Two-way Joist System 2-11

Chapter 3One-way Slabs 3-1

3.1 Overview 3-1

3.2 Determining the Slab Thickness 3-1

3.3 Detailing Requirements and Guidelines 3-1 for Flexural Reinforcement

3.3.1 Overview 3-1

3.3.2 Concrete Cover 3-1

3.3.3 Distribution of Flexural Reinforcement 3-2 for Crack Control

3.3.4 Minimum Spacing of Flexural 3-2 Reinforcement

3.3.5 Development of Longitudinal 3-2 Reinforcement, Flexural Cutoff Points, and Splices

Chapter 4Two-way Slabs 4-1

4.1 Overview 4-1

4.2 Determining the Slab Thickness 4-1


4.3.1 Overview 4-2


4.3.3 Minimum and Maximum Bar Spacing 4-2

4.3.4 Corner Reinforcement 4-2


4.3.6 Guidelines for Detailing the Flexural 4-3 Reinforcement

4.3.7 Openings in Slab Systems 4-4

4.4 Detailing Requirements and Guidelines 4-4 for Shear Reinforcement

4.4.1 Overview 4-4

4.4.2 Single- or Multiple-leg Stirrups 4-5

4.4.3 Headed Shear Studs 4-5

4.5 Detailing Requirements and Guidelines 4-6 for SDC C

Chapter 5Beams 5-1

5.1 Overview 5-1

5.2 Sizing the Cross-section 5-1

5.2.1 Beam Depth 5-1

5.2.2 Beam Width 5-1


5.3.1 Overview 5-2


5.3.3 Distribution of Flexural Reinforcement 5-2 for Crack Control

5.3.4 Minimum Spacing of Flexural 5-3 Reinforcement


5.4 Detailing Requirements and Guidelines 5-5 for Shear Reinforcement

5.4.1 Overview 5-5

5.4.2 Stirrup Configurations 5-5

5.4.3 Development of Shear Reinforcement 5-7

iiiConcrete Reinforcing Steel Institute



Contents5.5 Detailing Requirements and Guidelines 5-8

for Torsional Reinforcement

5.5.1 Overview 5-8

5.5.2 Detailing Requirements and Guidelines 5-9 for the Transverse Reinforcement

5.5.3 Detailing Requirements and Guidelines 5-9 for the Longitudinal Reinforcement

5.5.4 Detailing Requirements and Guidelines 5-9 for Combined Effects

5.6 Steps in Beams 5-10

5.6.1 Overview 5-10

5.6.2 Top Steps 5-10

5.6.3 Bottom Steps 5-11

5.6.4 Deep Steps 5-11


5.7.1 Overview 5-11

5.7.2 Design for Flexure 5-11

5.7.3 Design for Shear 5-12

5.8 Detailing Requirements and Guidelines 5-13 for SDC D, E, or F

5.8.1 Overview 5-13

5.8.2 Dimensional Limits 5-13

5.8.3 Design for Flexure 5-13

5.8.4 Design for Shear 5-13

5.9 Beams Not Designated as Part of the SFRS 5-14

Chapter 6Columns 6-1

6.1 Overview 6-1

6.2 Preliminary Column Sizing 6-1

6.3 Detailing Requirements and Guidelines 6-2 for Longitudinal Reinforcement

6.3.1 Overview 6-2

6.3.2 Minimum Number of Longitudinal Bars 6-2

6.3.3 Spacing of Longitudinal Bars 6-2

6.3.4 Splices 6-3

6.4 Detailing Requirements and Guidelines 6-3 for Transverse Reinforcement

6.4.1 Overview 6-3

6.4.2 Spiral Reinforcement 6-3

6.4.3 Tie Reinforcement 6-4

6.5 Detailing Requirements and Guidelines 6-7 for Dowels


6.6.1 Overview 6-8

6.6.2 Longitudinal Reinforcement Requirements 6-8

6.6.3 Transverse Reinforcement Requirements 6-8


6.7.1 Overview 6-9

6.7.2 Dimensional Limits 6-9

6.7.3 Longitudinal Reinforcement Requirements 6-9

6.7.4 Transverse Reinforcement Requirements 6-9

6.8 Columns Not Designated as Part of the SFRS 6-11

Chapter 7Walls 7-1

7.1 Overview 7-1

7.2 Determination of Wall Thickness 7-1

7.3 Minimum Reinforcement 7-1

7.4 Detailing Requirements and Guidelines 7-2 for Reinforcement

7.4.1 Overview 7-2


7.4.3 Spacing Requirements 7-2

7.4.4 Lateral Support of Longitudinal 7-2 Reinforcement

7.4.5 Wall Openings 7-3

7.4.6 Wall Corners and Intersections 7-4


7.5.1 Overview 7-7

7.5.2 Web Reinforcement Requirements 7-7

7.5.3 Boundary Elements 7-8

Chapter 8Diaphragms 8-1

8.1 Overview 8-1

8.2 Determing the Diaphragm Thickness 8-1

8.3 Detailing Requirements and Guidelines 8-1 for Reinforcement


8.4.1 Overview 8-2

8.4.2 Minimum Thickness 8-2

8.4.3 Minimum Reinforcement 8-2

iv Concrete Reinforcing Steel Institute



Chapter 9Foundations 9-1

9.1 Overview 9-1

9.2 Spread Footings 9-1

9.2.1 Material Selection 9-1

9.2.2 Determining the Base Dimensions and 9-1 Thickness

9.2.3 Detailing Requirements and Guidelines 9-1 for Reinforcement

9.3 Mat Foundations 9-3

9.3.1 Overview 9-3

9.3.2 Determining the Mat Thickness 9-3


9.4 Drilled Piers 9-4

9.4.1 Overview 9-4

9.4.2 Determining the Shaft Diameter 9-5

9.4.3 Determining the Bell Diameter 9-5


9.5 Grade Beams 9-7


9.6.1 Overview 9-9

9.6.2 Footings and Foundation Mats 9-9

9.6.3 Grade Beams 9-10

9.6.4 Piles, Piers, and Caissons 9-10

Chapter 10References 10-1

Notations N-1

vConcrete Reinforcing Steel Institute



CHAPTER 1 Introduction

1.1 OverviewOne of the main advantages of reinforced concrete is the ability to mold it into essentially any shape or form. There are no inherent restrictions that limit imagination and creativ-ity when it comes to the aesthetic design of a reinforced concrete structure. Along with the freedom of shape and form comes the reality of cost. A finite budget is the norm on the vast majority of projects that are undertaken and the cost of a structure can be needlessly larger than it has to be if there is not a basic understanding of what it takes to achieve overall economy in a reinforced concrete structure.

The purpose of this Guide is twofold:

• To present information on how to select an economical reinforced concrete floor system.

• To present requirements and guidelines on how to size, design, and detail reinforced concrete structural members that, where implemented, will result in an economical reinforced concrete structure.

The emphasis here is on building structures, but some of the information that is presented can be used in the design of bridges and other nonbuilding structures.

It is assumed that the reader has a basic understanding of the design and detailing of reinforced concrete structural members for combinations of gravity and lateral loads in accordance with the requirements of ACI 318, Building Code Requirements for Structural Concrete. This Guide is not a com-prehensive design guide on the fundamentals of reinforced concrete design. Rather, the information that is presented here is to be used by a design professional that will help in achieving overall economy in a reinforced concrete structure.

1.2 ScopeChapter 2 of this Guide contains general guidelines and information on how to select an economical reinforced con-crete floor system. In particular, wide-module joist, flat plate, flat slab, and two-way joist systems are covered. Tables are provided that give relative cost indices of floor systems for various span and load conditions. This information can help in determining the most economical system for a given set of constraints.

Chapters 3 through 9 present requirements and guidelines for sizing, designing, and detailing the following structural members:

• One-way slabs

• Two-way slabs

• Beams

• Columns

• Walls

• Diaphragms

• Foundations

Included in the discussion for each member type are the specific design and detailing requirements that are applicable to structures in areas of high seismic risk, that is, structures assigned to seismic design category (SDC) D, E, or F. Em-phasis is placed on constructability, which has a direct link to economy.

The references that are cited in this Guide can be found in Chapter 10.

Throughout the chapters, reference is made to the provisions of the 2014 edition of ACI 318, Building Code Requirements for Structural Concrete (Reference 1). For example, reference to Section 8.3 in ACI 318-14 is denoted here as ACI 8.3. A similar designation is provided for tables and figures from that document.

1-1Concrete Reinforcing Steel Institute



CHAPTER 2 Economical Reinforced Concrete Floor Systems

2.1 OverviewGeneral information is provided in this chapter on how to choose an economical reinforced concrete floor system and once chosen, how to achieve cost-savings when designing and detailing the structural members in the system. Tables are presented that can be utilized in selecting an economical system for a given set of constraints.

2.2 General Guidelines for Economical Reinforced Concrete Floor Systems

2.2.1 Overview

Through careful planning and detailing, the overall cost of the structure of a building utilizing reinforced concrete can be reduced considering the overall costs related to the main com-ponents of any reinforced concrete building, which are form-work, reinforcement, and concrete. The costs associated with formwork are generally 40 to 60 percent of the completed structure. Material costs for the concrete and reinforcement range from 10 to 30 percent of the overall cost. The labor cost for placing the concrete and reinforcement is the remainder.

This section covers general guidelines that will result in more economical reinforced concrete structures. Specific cost-sav-ing guidelines and techniques are given in the next section and the following chapters of this Guide for particular reinforced concrete floor systems and reinforced concrete members.

2.2.2 Formwork

By definition, formwork is the total system of support for freshly placed concrete, which includes the mold or sheathing that is in contact with the concrete and all of the supporting members, hardware, and bracing.

Project specifications can have a major impact on formwork design and speed of construction. Examples include stripping time, tolerances, concrete finish requirements, strength of concrete at time of form removal, and reinforcing steel and ac-cessory requirements. It is important that these items, as well as any other pertinent ones, be discussed with the concrete contractor as early as possible.

Because formwork and the labor associated with it are typi-cally the largest cost in a reinforced concrete structure, it is important to follow some basic guidelines, which when implemented, can result in overall cost savings. The following guidelines, which are not meant to be comprehensive, should be considered at the onset of any project.

1. Select one framing system and use it throughout

the structure wherever possible. Using the same framing system as often as practical throughout the structure has been shown to result in significant cost savings. Forms are reused many times and it is easier

for the crew when erecting the forms, resulting in reduced labor costs. In cases where multiple framing systems are specified, a separate forming system is needed for each system, which translates to additional costs associated with material and its mobilization. There are obvious exceptions to this guideline, particu-larly in areas of a building that have different usages. For example, it would be practical to have one framing system for the parking levels in a building and another for the typical residential or office floors.

2. Use standard shaped forms. Rectilinear members are the most cost effective to form. Whenever possible, avoid shapes that have to be either fabricated by the form supplier or customized by carpenters in the field. Large field fabrication costs can be incurred, for ex-ample, when the forms have to be modified for tapered members or for haunches.

Column capitals and drop panels are usually expensive to form. Consider using shear reinforcement to aug-ment two-way shear capacity of a slab.

3. Use modular formwork whenever practical. Tradi-tionally, modular forms have been used for floors and walls where the forms can be moved in large sections and reused often (usually between 10 and 20 times). Such proprietary forming systems have become more common and are being used to form smaller members. This type of formwork can also be used in customized applications such as slip-formed shafts for elevators and stairways and curved exterior walls. The cost of using such specialized forms can usually be justified if they can be reused multiple times in a project.

4. Use floor framing systems of minimum depth with

a constant elevation for the bottom surface of the

system. For most residential and office applications, the depth of the floor system is governed by service-ability (deflection) considerations. Providing the mini-mum depth based on these requirements will result in minimum floor-to-floor heights and, thus, an overall reduction in the building height. Overall height reduction translates to a reduction in the costs associated with essentially all of the vertical runs in the building (façade; elevators; stairs; interior partition walls; and plumbing, electrical, and mechanical conduit and ductwork).

The underside of a reinforced concrete floor or roof should be kept level for maximum economy. Sloping of floor or roof surfaces should be accomplished by vary-ing the structural slab thickness or by using concrete fill. Depressions for floor coverings should be made by varying the top surface of the slab rather than by adjust-ing formwork beneath the slab.




Fig. 2.1 Dowel Bar Mechanical Splice.

5. Orient one-way structural members to span in the

same direction throughout the entire structure. Experi-ence has shown that structures that have one-way mem-bers oriented in the same direction throughout the entire structure tend to be constructed more efficiently than those where multiple framing directions are used. This is attributed to less confusion and fewer mistakes made in the field because of the overall regularity of the structure.

6. Arrange columns in a regular pattern. If possible, the columns should be arranged in a regular pattern through-out each floor of the structure. This helps in achieving consistency in the formwork and reinforcement layout of all the structural members. Installing the formwork in such cases is repetitive and efficient and the formwork can be reused easily. This repetitiveness and efficiency carries over to all aspects related to the reinforcing bars.

7. Use a consistent column size. Experience has shown that it is more efficient to limit the number of changes in the column sizes throughout the height of a structure. In low-rise buildings, the same column size should be used throughout the entire height as should the same compres-sive strength of the concrete; the number of reinforcing bars can change over the height as needed. In taller build-ings, the same column size should be used over a number of floors and then changed accordingly over the height depending on the total number of stories in the building. The concrete compression strength and the number of reinforcing bars vary over the height as well.

8. Specify the time when forms may be stripped for self-

supporting members and the strength when forms may

be stripped for other members. Forms for columns and walls can be stripped based on time after the concrete has been placed (e.g., 12 hours). For beams and slabs, forms can be stripped after a specific percentage of concrete compres-sive strength has been attained (e.g., 75% of the specified 28-day compressive strength). It is important to note that beams and slabs must be reshored until the compressive strength has been attained to minimize deflections. Ap-propriate stripping specifications will minimize the required amount of formwork and will result in lower formwork costs.

9. Use high early strength concrete. The use of high early strength concrete enables the formwork to be stripped sooner than conventional concrete. Faster cycle times may allow for a faster overall construction time, which translates to significant overall cost savings.

10. Use predetermined construction joints. The location for construction joints should be the contractor’s prerogative with input from the engineer of record where required. Properly located construction joints will allow the contrac-tor to sequence concrete placement efficiently. The use of dowel bar mechanical splices at construction joints should be considered (see Fig. 2.1). This splice type contains a flange that is nailed to the forms. After the forms are stripped, the adjoining reinforcement can be screwed into the coupler. This eliminates bar or dowel penetration through the forms.

2.2.3 Reinforcement

1. Use Grade 60 reinforcing bars. ASTM A615 Grade 60 bars are the most widely used and inventoried reinforcing bars. Specifying Grade 40 bars may require 50% more steel than using Grade 60 bars. ASTM A615 Grade 75 or 80 bars are readily available, but are not normally inventoried by fabricators. It is important to note that these bars are usually available on mill orders ranging from 25 to 75 tons per bar size. However, smaller quantities may be obtained from warehouses, if available. In taller structures, the use of Grade 75 or 80 longitudinal bars in columns may de-crease congestion at the joints and may reduce the num-ber of crossties because a smaller number of longitudinal bars would generally be required.

2. Use the largest bar size possible. Placing and fabrica-tion costs are minimized by using the largest practical bar sizes that satisfy both strength and serviceability requirements. It is important to keep in mind that a greater quantity of smaller bars may be required for crack control or for other serviceability issues.

3. Use straight bars wherever possible. Fabricating and placing straight bars is faster and easier than bent bars.

4. Use ACI standard bar bend types. Specify standard bar shapes and bends provided in Reference 2. Nonstandard bends disrupt shop routine and are more costly to fabricate.

5. Use bars in one plane. Wherever possible, reinforcing bars should have bends located in one geometric plane. Bars with bends in two or three planes are difficult and expensive to fabricate. Additionally, it is difficult to maintain proper field tolerances because adjustment of the bar in one direction impacts the tolerance in one or more of the other directions.

6. Use repetitive bar sizes and lengths. The standard length for reinforcing bars is 60 ft, although some fabricators stock shorter lengths. In general, the longest available (and possible) bar lengths should be used to reduce fabrication and placing costs. Also, the number of bar sizes specified in a particular project should be minimized. This reduces the number of sizes that must be handled in the shop and placed in the field.

2-2 Concrete Reinforcing Steel Institute



Lap Varies,

7 1/

2"

#3 closedstirrups3-#6 T&B

6"

Beam Detail (Conceptual) Beam Detail (Scaled)

Interferencebetweenstirrups &top bars

Insufficentclear distancebetween bars

Fig. 2.2 Using Stock Length Bars Cut and Spliced in the Field.

Fig. 2.3 Beam Detail, Conceptual and Scaled.

7. Use stock length bars. In the case of irregularly-shaped walls and slabs, it is usually more cost effec-tive to use stock length bars that are cut and spliced in the field in lieu of using individual bars that have been sheared to a required length (see Fig. 2.2). The added cost associated with the extra material used due to vari-able lap lengths is usually minor and is more than offset by the savings due to reduced labor that would other-wise be required to cut and sort the individual bars.

8. Use the appropriate splice in the appropriate situ-

ation. Wherever possible, bars should be lap spliced. A consistent lap splice length should be specified for a given bar size. For columns utilizing #14 and #18 bars, and for #11 and smaller bars where congestion is an issue, use mechanical splices. A compression mechani-cal splice should be specified for bars that will always be in compression because these types of splices are considered to be the fastest to install in the field.

9. Provide a 4- to 6-in. gap to place concrete where

bars are closely spaced. In heavily reinforced mem-bers, such as transfer girders, where the spacing between bars is relatively close, provide a gap of 4 to 6 in. between bars, if possible. Based on experience, a 4-in. slump concrete with 3/4-in. aggregate will not flow easily though a 2-in. space between bars. Also, vibrator heads, which are usually 2 to 3 in. in width, may not fit between the bars or can become entangled in the bars if the space between bars is too small.

10. Draw details to scale to ensure that the reinforcing

bars will fit within the section. Scaled drawings that show all of the reinforcement are essential, especially in the following cases:

• Narrow beams

• Slabs with multiple openings, especially near sup-ports and edges

• Slab-column and beam-column joints

• Columns with more than 2% longitudinal rein-forcement

It is important to include the overall dimensions of the reinforcing bars, as well as hook dimensions and bend radii when drawing the scaled details. Table 2.1 con-

tains a list of overall bar diameters. Hook dimensions and bend radii for standard hooks and stirrup/tie hooks are given in Chapter 6 of Reference 3.

Figure 2.3 illustrates how a scaled detail drawing can help identify problems. The conceptual beam detail with the reinforcement depicted as lines and dots is given in the figure as is the detail where the reinforcement has been drawn to scale. It can be seen in the scaled drawing that the stirrup hooks will likely interfere with the top bars and the minimum clearance between the bars may not be met.

Bar SizeApproximate Diameter Outside

Deformations, in.

#3 7/16#4 9/16#5 11/16#6 7/8#7 1

#8 11/8#9 11/4#10 17/16#11 15/8#14 17/8#18 21/2

SECT. ASECT. A

A A

OverallDiameter

NominalDiameter

Table 2.1 Overall Reinforcing Bar Diameter




2.2.4 Concrete

1. Use moderate-strength concrete. 4,000 to 5,000 psi compressive strength concrete is usually sufficient. Exceptions are for columns in high-rises and floor systems in which there are shear capacity issues. Columns, shear walls, and joints may require higher strength concrete to enhance their axial and flexural capacity.

2. Use high-performance concrete where placement

and consolidation is expected to be difficult. High-performance concrete is defined within ACI 116 as concrete meeting special combinations of performance and unifor-mity requirements that cannot always be achieved routinely using conventional constituents and normal mixing, placing, and curing practices. These requirements could potentially include the following enhancements:

• Ease of placement and consolidation without affecting strength;

• Long-term mechanical properties;

• Durability in severe environments;

• High early strength;

• Toughness;

• Volume stability.

These properties are usually achieved with special admix-tures, which alter the plastic properties and workability of the concrete during placement, making it less viscous (more fluid) than conventional concrete. Long-term strength prop-erties are usually unaffected.

Self-consolidating concrete (SCC) is a special type of high-performance concrete. It is defined by the National Ready-Mix Concrete Association (NRMCA) as a highly flowable, non-segregating concrete that can flow into place, fill the formwork, and encapsulate the reinforcement without any mechanical consolidation. In general, SCC is concrete made with conventional concrete materials and, in most cases, with a viscosity-modifying admixture (VMA). SCC is also useful in applications where high quality surface finishes are desired without bugholes or honeycombing. Increased form pressures may be generated when SCC is used, necessitat-ing possible changes in formwork design.

ACI Committee Report 237R (Reference 24) indicates that SCC provides the following features, which are equally ap-plicable to general high-performance concrete:

• It is good at replicating architectural form features;

• Free fall into the formwork can be greater than the conventional limit of 5 ft.;

• Less screeding operations are required to ensure flat surfaces (self-leveling characteristic);

• It facilitates accelerated construction, through higher rate of casting or placing and shorter construction duration;

• It facilitates and expedites the filling of highly rein-

forced sections and complex formwork while ensuring good construction quality which may lead to increased productivity, reduces the labor requirement and cost, or both;

• Improved flexibility in spreading placing points dur-ing casting. This can reduce the need for frequent movement of transit trucks and the need to move the pump lines to place concrete (possible reduction in the number of pumps, pump operators, and so on). This greater flexibility in scheduling construction activities and procuring the required resources results in both time and resource savings.

SCC may be evaluated in the field using a standard slump test; however, the slump cone is often inverted. Instead of measuring the distance between the top of the cone and the top of the sample, the puddle of concrete is measured in 2 orthogonal directions to determine the spread diameter. Standard slump mea-surements of highly flowable concrete is practically irrelevant, as it has no measureable slump (>> 12 in.). Other mixture evaluation tests include the J-ring test, used to evaluate the flow and segregation characteris-tics of high-performance concrete.

3. Use high-strength concrete in columns. High-strength concrete can be justified in columns if the use of higher strength concrete reduces the amount of longitudinal reinforcement. Similarly, column sizes can be reduced or just use one column size on a project. Specify the same strength concrete in all columns of a story, to minimize mistakes.

4. Specify few mix designs. On most projects only two strengths of concrete are necessary, a normal mix (4,000 to 5,000 psi) and a high-strength mix (8,000 psi or greater). Some projects may necessitate three.

Consistent with the construction shown in Figure 2.4, it is most economical to use the high-strength column concrete in the slab puddling zone. In an effort to optimize concrete mixes on a project, some engineers have specified a separate puddling mix, because ACI 318 only allows a design concrete strength of 10,000 psi in shear. Some high-strength column concretes may have compressive strengths ranging from 12,000 psi to 15,000 psi.

To make placement easier and avoid potential place-ment mistakes on the project, it is usually more economical to use the column concrete in the puddling zone, and design for a maximum concrete strength of 10,000 psi; a separate puddling mix is thus not recom-mended.

5. Limit coarse aggregate size to ¾ inch. As a matter of practice limit the coarse aggregate to ¾ inch since the minimum clear bar spacing is normally 1 inch and ACI 318 Code requires a clear distance of four-thirds the aggregate size.




Fig. 2.4 Concrete “Puddling” around Columns. Photo courtesy of Skidmore, Owings and Merrill LLP.

Column concrete placed in the nearby slab section.

2.3 Selecting an Economical Reinforced Concrete Floor System

2.3.1 Overview

Numerous types of cast-in-place, reinforced concrete floor systems are available to satisfy virtually any span and loading condition that is required. Because the cost of the floor sys-tem is often the major part of the structural cost of a building, selecting the most effective system for a given set of con-straints is vital in achieving overall economy. This is especially important for low- and mid-rise buildings and for buildings subjected to relatively low wind and seismic forces because the cost of the lateral force-resisting systems in such cases is minimal compared to the typical floor systems.

Provided in this chapter are preliminary estimates of mate-rial quantities for various cast-in-place reinforced concrete floor systems with a variety of span and loading conditions. In particular, the following conventionally reinforced concrete systems are covered:

• One-way joist

• Flat plate

• Flat slab

• Two-way joist (waffle)

Voided slabs are reinforced concrete slabs similar to flat plates that contain regularly-spaced voids. The voids are usually created using hollow recycled plastic void formers and are positioned in wire cages to create modules, which are placed between the top and bottom layers of flexural reinforcement in the slab. Both squat and spherical void formers are available in different sizes. The main purpose of the voids is to eliminate concrete in areas where it is not needed, thereby reducing the overall weight of the floor system. Voided slabs are not addressed in this Guide; more information can be found in Reference 4 and in manufacturers’ literature.

The structural members of the floor systems that are covered in this chapter were designed and detailed for the effects of gravity load in accordance with ACI 318-14 (Reference 1). CRSI’s Reinforced Concrete Concept, which is a preliminary design tool that provides material and cost estimates for a

variety of conventionally reinforced concrete floor systems, was used to generate the information provided in the follow-ing tables (http://concept.crsi.org/index.cfm). It is assumed that the members in the various floor systems are not part of the lateral force-resisting system. Span and loading conditions that are typical for residential and office buildings are included in the analysis.

In all cases, normal-weight concrete with a density of 150 pcf and a specified compressive strength of 4,000 psi is utilized. Also, Grade 60 reinforcing bars are used. The live load varies from 40 psf to 100 psf, and the superimposed dead load is taken as 10 psf in all cases.

Concrete, reinforcing steel, and formwork quantities are given in the tables for various span and loading conditions. In gen-eral, unlimited design solutions are possible for a given set of constraints. The member sizes in the tables for a particular bay size and superimposed loading satisfy all applicable ACI 318 requirements and were chosen based on the guidelines pre-sented in this Guide, practicality, experience, and formwork economy. This does not imply, however, the following: (1) the provided sizes result in the most economical solution because no mathematical attempt was made to optimize the overall cost of the floor system for a given set of constraints and (2) members sizes not contained in the tables are uneconomical and/or impractical and that they should not be considered for the case at hand.

Cost indices of the various floor systems are also provided in the tables. Unit in-place costs for concrete, reinforcement, and formwork used in this analysis were obtained from Reference 5. These unit costs, which include both materials and instal-lation, represent national average costs for major cities in the U.S. The cost index is the ratio of the total cost—in-place costs of concrete, reinforcement, and formwork for that particular case—to the average total cost of all cases in all systems considered in this Guide. These cost indices can be used to compare relative costs between different systems as a function of span and loading. The size and geographic location of the project, the availability of skilled labor, and local building code requirements are a few of the many factors that significantly af-fect costs. Thus, it is important to use the data in the tables as a preliminary guide in selecting an economical floor system.

2.3.2 One-way Joist System

Overview

A one-way joist floor system, which is commonly referred to as a wide-module joist system or a “skip” joist system when the clear spacing between the joist ribs exceeds 30 inches, consists of regularly spaced concrete joists (ribs) spanning in one direction, a reinforced concrete slab cast integrally with the joists, and beams (or, girders) that span between the col-umns, perpendicular to the joists (see Fig. 2.5). The joists are formed by using pan forms that are either 53 or 66 in. wide. Systems formed by the 66-in.-wide pans that range in depth between 14 and 24 in. are considered in this Guide.




Fig. 2.5 One-way Joist System.

The main advantages of a one-way joist system are: (1) they are economical for long spans with heavy loads, (2) the pan voids reduce the dead load, and (3) electrical and mechanical equipment can be placed between joists, which means the overall floor depth need not be increased to accommodate this equipment. The longer spans and inherent vibration resis-tance make this an attractive floor system for office buildings, hospitals, and schools.

It is important to note that wide-module joist construction does not satisfy the limitations of ACI 9.8.1 of standard joist systems; therefore, the members of the floor system are to be designed as one-way slabs and beams.

Member Sizes

The thickness of the slab spanning between the joists (beams) can be controlled by either structural or fire resis-tance requirements. Specifying a lightweight aggregate may be advantageous in certain situations because a 2-hour fire-resistance rating can be achieved with a relatively thin slab. This would also result in a reduction of dead load. A normal-weight concrete slab with a 4.5-in. thickness is used in all cases considered in this Guide.

One layer of reinforcement is usually provided in the slab at mid-depth perpendicular to the joists. The minimum amount of reinforcement required for temperature and shrinkage, as prescribed in ACI 7.6, usually governs.

The dimensions of the joists depend on deflection and strength requirements. The minimum thickness of nonpre-stressed beams that are not supporting or attached to parti-tions and other construction likely to be damaged by deflec-tions is given in ACI Table 9.3.1.1. According to this table, the slab thickness plus pan depth should be greater than or equal to 18.5 (exterior span) or 21 (interior span) in the case of normal-weight concrete and Grade 60 reinforcement, where is the span length defined in ACI Chapter 2. Table 2.2 contains the maximum span lengths for one-way joist systems, assuming a 4.5-in. thick slab.

Table 2.2 Maximum Span Lengths for One-way Joist Systems

with 66-in.-wide Pans

Pan Depth

(in.)

Exterior Span,

Maximum Span

Length, (ft)

Interior Span,

Maximum Span

Length, (ft)

14 28.5 32.4

16 31.6 35.9

20 37.8 42.9

24 43.9 49.9

The overall depths of the systems contained in the tables in the Summary section satisfy the requirements of ACI Table 9.3.1.1. A thickness less than that prescribed in this table is al-lowed if it can be demonstrated that computed deflections are less than or equal to the limits prescribed in ACI Table 24.2.2.

Once a thickness has been established, a joist width is chosen. The width of the joists can be tailored to satisfy virtually any requirement. In most cases, the thinnest practical joist width, for a given rib spacing, will be adequate for structural requirements. Bay sizes and floor layouts may also have an influence on the width of the joists. In certain cases, specific joist widths may be necessary in order to provide economical and practical formwork.

The thickness of the supporting beams (or, girders) is dictated by the thickness of the joists. To achieve overall formwork economy, the depth of supporting members should be the same as the overall depth of the joists. If additional capacity is required, beams should be made wider, not deeper. Also, beams should be wider than the columns into which they frame, if possible. In addition to assuring formwork economy, this also alleviates some of the reinforcement congestion that can occur at the joints.

In the tables in the Summary section below, the second to last column contains the pan area percentage, which is the percentage of the floor area that requires pan formwork.

Joist Orientation

Depending on span lengths and superimposed loads, it is usually more cost effective to span the joists in the long direction. This also helps in assuring that a level floor soffit is achieved because the beams are spanning in the short direction. For bays with as-pect ratios less than 1.5, the cost differential between joists fram-ing in the short direction and long direction is typically very small.

Live Load Effects

Material quantities are, to a large extent, controlled by deflection requirements. An increase in live loads does not have a proportional impact on cost. A live load of 100 psf results in an increase of less than 5% over the cost of a system designed for a live load of 40 psf.

Panel Aspect Ratio Effects

The aspect ratio of the slab panels has a minimal effect on material quantities for ratios less than 1.5. As noted above, spanning the joists in the long direction usually results in the most economical solution.




Summary

One-way joist systems are economically viable for medium to long spans with moderate to heavy loads. Systems formed with 66-in. pans are feasible for span lengths ranging from 35 to 50 ft and beyond. Large, column-free spaces can be achieved without vibration problems for typical residential and office occupancies.

Tables 2.3, 2.4, and 2.5 contain material quantities and cost indices for one-way joist systems with live loads of 40, 65, and 100 psf, respectively.

Table 2.3 Material Quantities and Cost Indices for One-way Joist Floor Systems, LL = 40 psf

Bay Size (ft)Pan Depth

(in.)

Beam Width

(in.)

Square

Column Size

(in.)

Concrete

(ft3/ft2)

Reinforce-

ment (psf)

Pan Area

(%)Cost Index

25 25 14 26 22 0.62 2.09 89 0.80

30 30 16 32 28 0.65 2.43 89 0.83

30 35 20 34 30 0.71 2.36 90 0.85

30 40 24 36 32 0.77 2.53 90 0.88

35 35 20 34 30 0.71 2.65 90 0.86

35 40 24 36 32 0.77 2.76 90 0.89

40 40 24 36 32 0.77 3.05 90 0.91



(in.)

Beam Width

(in.)

Square

Column Size

(in.)

Concrete

(ft3/ft2)

Reinforce-

ment (psf)

Pan Area

(%)Cost Index

25 25 14 28 24 0.62 2.49 88 0.82

30 30 16 34 30 0.65 2.73 88 0.84

30 35 20 36 32 0.71 2.75 89 0.87

30 40 24 38 34 0.77 2.70 90 0.89

35 35 20 36 32 0.71 3.16 89 0.89

35 40 24 38 34 0.77 3.00 90 0.90

40 40 24 38 34 0.77 3.36 90 0.92



(in.)

Beam Width

(in.)

Square

Column Size

(in.)

Concrete

(ft3/ft2)

Reinforce-

ment (psf)

Pan Area

(%)Cost Index

25 25 14 30 26 0.63 2.82 87 0.84

30 30 16 36 32 0.66 3.41 87 0.88

30 35 20 38 34 0.72 3.18 89 0.89

30 40 24 40 36 0.78 3.29 89 0.92

35 35 20 38 34 0.72 3.67 89 0.92

35 40 24 40 36 0.78 3.70 89 0.94

40 40 24 40 36 0.78 4.10 89 0.96




Fig. 2.6 Flat Plate.

2.3.3 Flat Plate System

Overview

A flat plate floor system is a two-way concrete slab supported directly on columns with reinforcement in two orthogonal directions (see Fig. 2.6). Primarily used in hotels, multi-family residential buildings, and office buildings, this system has the advantages of simple construction and formwork and a flat ceiling, the latter of which reduces ceiling finishing costs because the architectural finish can be applied directly to the underside of the slab. Even more significant are the cost savings associated with the low story heights made possible by the shallow floor system. Smaller vertical runs of cladding, partition walls, mechanical systems, plumbing, and other primarily vertical items of construction translate to large cost savings, especially for medium- and high-rise buildings. More-over, where the total height of a building is restricted, using a flat plate can result in more stories accommodated within the set height.

Minimum Slab Thickness

Minimum slab thickness requirements for flat plates are given in ACI Table 8.3.1.1. The minimum thickness of exterior and interior panels of flat plates without edge beams and contain-ing reinforcement with a yield strength of 60,000 psi is equal to n 30 and n 33, respectively, where n is the length of the clear span in the long direction. The panel that yields the larg-est thickness is used throughout the entire floor plate. In no case should the thickness be less than 5 in.

Live Load Effects

For live loads of 40 psf or less, the thickness of the slab will usually be controlled by deflection requirements. Also, the flexural reinforcement at the critical sections in the column and middle strips will be about the minimum amount pre-scribed in ACI Table 8.6.1.1. Thus, using a slab thickness greater than the minimum allowable thickness is not economi-cal because a thicker slab will increase the concrete quantity and not reduce the reinforcement quantity. Note that mini-mum thickness requirements are independent of the concrete

compressive strength. Specifying a compressive strength greater than 4,000 psi will increase the cost of the concrete without any allowable reduction in slab thickness. Therefore, for live loads of 40 psf or less, the most economical flat plate floor system is one where a minimum thickness computed by ACI Table 8.3.1.1 and a concrete compressive strength of 4,000 psi are specified.

For live loads of 100 psf or more, the thickness of the slab will more than likely be controlled by the two-way shear stresses at the critical section around the columns and the bend-ing moments in the slab, and not by the deflection criteria described above. Thicker slabs are generally provided to resist the larger shear stresses due to larger live loads. Although a thicker slab may result in a decrease in the required amount of flexural reinforcement, the reduction in the cost of reinforce-ment will not offset the increase in the cost of concrete. Also, using a higher strength concrete is not the most effective way of increasing the nominal moment strength and, more importantly, the nominal two-way shear strength provided by the concrete at the critical section around the columns. Cost analyses show that the cost of a flat plate system with a concrete strength greater than 4,000 psi is greater than the cost of one with a compressive strength of 4,000 psi, even when reductions in thickness and/or reinforcement are taken into consideration for the systems with the higher strength concrete. Therefore, for live loads of 100 psf and greater, the most cost-effective solution is to use a slab thickness equal to the minimum required for strength and a concrete compres-sive strength equal to 4,000 psi. The use of shear studs to counteract the effects of two-way shear stresses is discussed in Chapter 4 of this Guide.


The aspect ratio of a slab panel is defined as the larger dimension of the panel divided by the smaller dimension of the panel, measured center-to-center of supports. Where the aspect ratio exceeds 2, the slab acts primarily as a one-way slab spanning in the short direction.

As discussed above, the minimum slab thickness is depen-dent on the clear span length. The slab thickness require-ment is the same in both directions for square bays. For an aspect ratio other than 1, the longer span will dictate the slab thickness, resulting in a loss of economy. A floor system that contains rectangular bays with an aspect ratio of 2 costs ap-proximately 30% more than one with an aspect ratio of 1, for the same overall floor area. Unless column layout is dictated by architectural or other functional requirements, square bays should be used because they provide the most economical layout.

Summary

Flat plate systems are economically viable for short to medium spans and for moderate live loads. The deflection criteria usually govern up to live loads of about 40 psf, and the economical span length range is 15 to 30 ft. For live loads of 100 psf or more, two-way shear stresses at the columns and




Fig. 2.7 Flat Slab.

bending moments in the slab control the design. For these cases, the flat plate is economical for spans between 15 and 25 ft.

Tables 2.6, 2.7, and 2.8 contain material quantities and cost indices for flat plate systems with live loads of 40, 65, and 100 psf, respectively.

Table 2.6 Material Quantities and Cost Indices for Flat Plate Floor Systems, LL = 40 psf

Bay Size (ft)Slab Thickness

(in.)

Square Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)Cost Index

15 15 6.0 12 0.50 1.62 1.00 0.78

15 20 7.5 14 0.63 1.89 1.00 0.83

20 20 7.5 16 0.63 1.92 1.00 0.83

20 25 9.5 18 0.79 2.35 1.00 0.91

25 25 9.5 22 0.79 2.45 1.00 0.91



(in.)

Square Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)Cost Index

15 15 6.0 14 0.50 1.71 1.00 0.78

15 20 7.5 16 0.63 1.99 1.00 0.84

20 20 7.5 20 0.63 2.07 1.00 0.84

20 25 9.5 22 0.79 2.50 1.00 0.92

25 25 9.5 26 0.79 2.61 1.00 0.92



(in.)

Square Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)Cost Index

15 15 6.0 16 0.50 1.88 1.00 0.79

15 20 7.5 18 0.63 2.17 1.00 0.85

20 20 7.5 24 0.63 2.31 1.00 0.85

20 25 9.5 26 0.79 2.75 1.00 0.93

25 25 9.5 30 0.79 2.94 1.00 0.94

2.3.4 Flat Slab System

Overview

A flat slab floor system is similar to a flat plate floor system, with the exception that the flat slab has thickened portions around the columns called drop panels (see Fig. 2.7). The primary purpose of the drop panels is to increase the nominal two-way shear strength of the concrete at the critical section around the columns. The flat slab system has the advantages of relatively simple construction and formwork, low floor-to-floor heights, and a relatively flat ceiling, which allows an architectural finish to be applied directly to the underside of the slab. This system is primarily used in buildings with mod-erate to heavy loads, such as office buildings, hospitals, and warehouses.




Fig. 2.8 Minimum Drop Panel Dimensions.

Minimum Slab Thickness and Drop Panel Dimensions

Minimum slab thickness requirements for flat slabs are given in ACI Table 8.3.1.1. The minimum thickness of exterior and interior panels of slabs with drop panels defined in ACI 8.2.4, without edge beams, and containing reinforcement with a yield strength of 60,000 psi is equal to n 33 and n 36, re-spectively, where n is the length of the clear span in the long direction. It is evident that the minimum thickness of flat slabs is 10% less than that required for flat plates; this is primarily due to the decrease in deflection from the addition of the drop panels around the columns. In no case should the slab thick-ness be less than 4 in.

Minimum dimensions for drop panels are given in ACI 8.2.4. The drop panel should extend in each direction from the centerline of the support a distance not less than one-sixth of the span length measured from center-to-center of supports in that direction (see Fig. 2.8). Also, the projection of the drop panel below the slab should be at least one-quarter of the slab thickness. The minimum slab thickness must be increased by 10% if drop panel dimensions are provided that do not conform to these provisions.

To achieve formwork economy, standard lumber dimensions should be used to form the drop panels. Table 2.9 contains drop panel heights based on actual lumber dimensions and 3/4-in.-thick formwork sheathing. Using other depths will un-necessarily increase formwork costs.

In the preliminary design stage, a slab thickness is chosen based on the minimum thickness requirements of ACI Table 8.3.1.1. The plan dimensions of the drop panel are then deter-mined based on the minimum lengths specified in ACI 8.2.4. Two-way shear stresses at the critical section around the column should be checked for a minimum drop depth of 2.25 in. If this proves to be inadequate, the next larger drop depth (4.25 in.) should be used until the shear strength require-ments are satisfied. According to ACI 22.6.4, shear stresses must be checked at the critical sections around the columns and the drop panels.

Live Load Effects

The material quantities for a flat slab are typically controlled by deflections. Therefore, an increase in live loads will not cause a proportional increase in costs. Flat slab systems subjected to live loads of 100 psf are usually 3 to 7% more expensive than those with live loads of 40 psf.


Square bay sizes with an aspect ratio equal to 1 represent the most economical floor layout because the required minimum slab thickness is the same in both directions. A rectangular bay with an aspect ratio of 1.2 is about 17% more expensive than a square bay with the same floor area.

Summary

Flat slab systems are economically viable for medium spans and for moderate to heavy live loads. For a live load of 65 psf or less, flat slabs are cost-effective for span lengths between 30 ft and 35 ft. The economical range is 25 ft to 35 ft for a live load of 100 psf. Although the drop panels result in somewhat higher formwork costs, a relatively shallow slab system is achieved in situations where two-way shear stresses would otherwise preclude the use of a flat plate.

Tables 2.10, 2.11, and 2.12 contain material quantities and cost indices for flat slab systems with live loads of 40, 65, and 100 psf, respectively.

Standard Lumber Dimensions and Drop Panel Height

Lumber Size Drop Panel

Height, h1*

Nominal Actual

2x 11/2" 21/4"

4x 31/2" 41/4"

6x 51/2" 61/4"

8x 71/4" 8"

* 3/4"-inch form sheathing

Table 2.9 Drop Panel Height for Formwork Economy




Fig. 2.9 Two-way Joist (Waffle Slab).

2.3.5 Two-way Joist System

Overview

A two-way joist system, which is also commonly referred to as a waffle slab, consists of evenly spaced concrete joists spanning in both directions and a reinforced concrete slab cast integrally with the joists (see Fig. 2.9). The floor system is formed with domes that are 30, 41, and 52 in. wide, resulting in 3-, 4-, and 5-ft modules, respectively. Systems with a 3-ft module are considered in this Guide. A solid slab section around the columns is usually provided for two-way shear resistance.

Table 2.10 Material Quantities and Cost Indices for Flat Slab Floor Systems, LL = 40 psf

Bay

Size (ft)

Slab

Thickness

(in.)

Drop Size Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)

Cost

IndexL W

(ft)

h1

(in.)

20 20 7.0 7 7 2.25 14 0.61 2.01 1.01 0.84

20 25 8.5 7 81/2 2.25 16 0.73 2.23 1.01 0.89

25 25 8.5 81/2 81/2 2.25 18 0.73 2.36 1.01 0.90

25 30 10.5 81/2 10 4.25 20 0.92 2.82 1.02 0.99

30 30 10.5 10 10 4.25 24 0.92 2.99 1.02 0.99

30 35 12.0 10 12 4.25 26 1.04 3.44 1.02 1.06

35 35 12.0 12 12 4.25 30 1.05 3.69 1.01 1.07


Bay

Size (ft)

Slab

Thickness

(in.)

Drop Size Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)

Cost

IndexL W

(ft)

h1

(in.)

20 20 7.0 7 7 2.25 16 0.61 2.15 1.01 0.85

20 25 8.5 7 81/2 2.25 18 0.73 2.47 1.01 0.91

25 25 8.5 81/2 81/2 2.25 22 0.73 2.66 1.01 0.91

25 30 10.5 81/2 10 4.25 24 0.92 3.09 1.02 1.00

30 30 10.5 10 10 4.25 26 0.92 3.37 1.02 1.02

30 35 12.0 10 12 4.25 30 1.05 3.76 1.02 1.08

35 35 12.0 12 12 4.25 34 1.05 4.09 1.01 1.09


Bay

Size (ft)

Slab

Thickness

(in.)

Drop Size Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Formwork

(ft2/ft2)

Cost

IndexL W

(ft)

h1

(in.)

20 20 7.0 7 7 2.25 20 0.61 2.44 1.01 0.87

20 25 8.5 7 81/2 2.25 22 0.73 2.79 1.01 0.92

25 25 8.5 81/2 81/2 2.25 26 0.73 3.08 1.01 0.94

25 30 10.5 81/2 10 4.25 28 0.92 3.47 1.02 1.02

30 30 10.5 10 10 4.25 32 0.92 3.85 1.02 1.04

30 35 12.0 10 12 4.25 34 1.06 4.22 1.02 1.10

35 35 12.0 12 12 6.25 40 1.07 4.68 1.02 1.14




The main advantages of this type of system are that they are economical for long spans with heavy loads, the dome voids reduce the dead load, and electrical fixtures or other items can be placed in the voids. It is common for these systems to be exposed so architectural finishes are usually not required, which results in cost savings. Two-way joist systems are com-monly used in office buildings, warehouses, libraries, civic buildings, and industrial plants.

Member Sizes

The thickness of the slab is controlled by either structural or fire resistance requirements. In most cases, the thickness is governed by the latter. Specifying a lightweight aggregate may be advantageous in certain situations. A normal-weight slab with a 4.5-in. thickness is used in all cases considered in this Guide.

The standard joist width is 6 in. for a 3-ft module. Because slab thickness is controlled by fire resistance requirements and joist width is set by industry standards, the only geomet-ric variable to be determined is joist depth. Standard dome depths for the 3-ft module are 8, 10, 12, 14, 16, 20 and 24 in.

For design purposes, waffle slabs are considered as flat slabs with the solid heads acting as drop panels. Thus, the minimum thickness of exterior and interior panels of two-way slabs with drop panels defined in ACI 8.2.4, without edge beams, and containing reinforcement with a yield strength of 60,000 psi is equal to n 33 and n 36, respectively, where n is the length of the clear span in the long direction. In no case should the slab thickness be less than 4 in. To determine the deflection requirements, the cross-section of the actual floor system is transformed into an equivalent section of uniform thickness. This is accomplished by determining a slab thickness that provides the same moment of inertia as the two-way joist section. Table 2.13 contains the equivalent slab thickness for the standard domes depths of a 3-ft module waffle slab.

Table 2.13 Equivalent Slab Thickness for Two-way Joists

with a 3-ft Module

Dome Depth

(in.)

Rib Width

(in.)

Equivalent Slab

Thickness (in.)

8 6 8.8

10 6 10.3

12 6 11.7

14 6 13.1

16 6 14.6

20 6 17.4

24 6 20.2

In the tables in the Summary section below, the second to last column contains the dome area percentage, which is the percentage of the floor area that requires dome formwork.

Live Load Effects

Because material quantities are typically controlled by deflec-tion constraints, an increase in live load does not have a proportionate impact on costs. Waffle slabs with live loads of 100 psf are typically only 3 to 7% more expensive than those with live loads of 40 psf.


Square bay sizes are the most cost-effective because the deflection requirements are the same in both directions. A rectangular bay with an aspect ratio of 2 is about 15% more expensive than a square bay with the same floor area.

Summary

Two-way joist systems are economically viable for long spans and heavy loads. Systems with 3-ft modules are usually eco-nomical for spans ranging from 40 to 50 ft and beyond.

Tables 2.14, 2.15, and 2.16 contain material quantities and cost indices for two-way joist systems with live loads of 40, 65, and 100 psf, respectively.




Table 2.14 Material Quantities and Cost Indices for Two-way Joist Floor Systems, LL = 40 psf

Bay

Size (ft)

Dome

Depth (in.)Solid Head

Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Dome Area

(%)

Cost

Index

30 30 10 12'-6" 12'-6" 24 0.81 1.97 84 1.11

36 36 14 14'-6" 14'-6" 28 0.98 2.37 86 1.19

36 42 16 14'-6" 16'-6" 30 1.09 2.75 86 1.24

42 42 16 16'-6" 16'-6" 30 1.10 2.91 86 1.26

48 48 20 18'-6" 18'-6" 32 1.30 3.85 85 1.37

51 51 20 20'-6" 20'-6" 38 1.27 4.07 86 1.37


Bay

Size (ft)

Dome


Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Dome Area

(%)

Cost

Index

30 30 10 12'-6" 12'-6" 24 0.81 2.12 84 1.12

36 36 14 14'-6" 14'-6" 28 0.98 2.83 86 1.21

36 42 16 14'-6" 16'-6" 30 1.09 2.94 86 1.25

42 42 16 16'-6" 16'-6" 32 1.10 3.11 86 1.27

48 48 20 18'-6" 18'-6" 38 1.31 4.04 85 1.38

51 51 20 20'-6" 20'-6" 44 1.28 4.24 86 1.38


Bay

Size (ft)

Dome


Square

Column

Size (in.)

Concrete

(ft3/ft2)

Reinforcement

(psf)

Dome Area

(%)

Cost

Index

30 30 10 12'-6" 12'-6" 26 0.81 2.85 84 1.16

36 36 14 14'-6" 14'-6" 30 0.98 3.05 86 1.22

36 42 16 14'-6" 16'-6" 34 1.09 3.13 86 1.26

42 42 16 16'-6" 16'-6" 38 1.10 3.96 86 1.31

48 48 20 18'-6" 18'-6" 44 1.31 4.28 85 1.40

51 51 20 20'-6" 20'-6" 50 1.28 5.30 86 1.44




Fig. 3.1 Slab with Drip Groove at Edge of Soffit (a) Cover is Maintained at Drip Groove by Offsetting the Bottom Longitudinal Bars (b) Cover is Maintained at Drip Groove by Relocating Longitudinal Bars.

CHAPTER 3 One-way Slabs

3.1 OverviewGuidelines and recommendations on the economical design and detailing of one-way slabs are contained in this chapter. Information is provided on determining the thickness of the slab and detailing the flexural reinforcement.

Shear reinforcement is typically not provided in one-way slabs. The design shear strength can be increased by providing a thicker slab and/or by increasing the compressive strength of the concrete, with the former being the most efficient solu-tion in cases where more than a relatively small amount of additional shear strength needs to be provided.

Because one-way slab systems are usually not part of the seismic force-resisting system (SFRS), the following require-ments and guidelines are essentially applicable for one-way slabs in buildings assigned to any SDC.

3.2 Determining the Slab ThicknessThe thickness of a one-way slab is usually determined initially based on the minimum thickness requirements in ACI 7.3.1. ACI Table 7.3.1.1 contains the minimum thickness h that must be provided as a function of the support conditions and the span length of the slab for normal-weight concrete and Grade 60 reinforcement in situations where the slab is not support-ing or attached to partitions or other construction likely to be damaged by large deflections.

For the usual case of continuous construction, the depth of the slab must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth. Specifying more than one slab depth results in formwork that is not economical.

It is also important to consider fire resistance requirements when specifying a slab thickness, especially for one-way slabs that are supported by joists, which are spaced relatively close-ly together. It is possible in certain cases that the required slab thickness based on fire resistance requirements needs to be greater than the minimum slab thickness determined by ACI Table 7.3.1.1 for serviceability.

3.3 Detailing Requirements and Guidelines for Flexural Reinforcement

3.3.1 Overview

Once the required area of flexural reinforcement has been determined for the factored bending moments along the span length using the strength design method, the size of reinforc-ing bars must be chosen to provide an area of steel that is greater than or equal to the amount that is required.

Additionally, minimum spacing between the flexural bars must be provided so that concrete can adequately flow in the voids between the bars. A maximum spacing between the flexural bars is required

to limit the size the flexural crack widths. Finally, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corrosive environments, to name a few.

The flexural reinforcement must be properly developed or an-chored on both sides of a critical section. This ensures that the one-way slab system will perform as intended in accordance with the strength design method.

Temperature and shrinkage reinforcement in accordance with ACI 24.4.3 must be provided perpendicular to the main flexural rein-forcement. ACI Table 24.4.3.2 contains minimum reinforcement ratios to counteract temperature and shrinkage stresses and ACI 24.4.3.3 stipulates the maximum spacing of such reinforcement.

3.3.2 Concrete Cover

Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonpre-stressed, cast-in-place concrete members are given in ACI Table 20.6.1.3.1. For one-way slabs, concrete cover is mea-sured from the surface of the concrete to the outer edge of the longitudinal reinforcement.

Drip grooves or drip edges along the edge of a slab soffit can cause issues related to the required cover to the longitudinal reinforcement. These grooves are usually formed using a form chamfer strip or a one-inch piece of dimension lumber nailed to the formwork deck near the slab edge. There are essentially two ways to maintain the required concrete cover in such cases (Ref-erence 6): (1) offset the bars crossing the groove (see Fig. 3.1a) and (2) relocate the transverse and longitudinal layers of reinforc-ing bars so that the affected reinforced bar (shown as an open circle in Fig. 3.1b) can be moved away from the groove, thereby maintaining the required minimum cover.




Fig. 3.2 Recommended Flexural Reinforcement Details for One-way Slabs.

Layering of the top steel in the slab over intersecting beams that are supporting the slab can create constructability issues for the detailer and placer. More information on this topic can be found in Section 5.3.2 of this Guide.

3.3.3 Distribution of Flexural Reinforcement for

Crack Control

Requirements for the distribution of flexural reinforcement in one-way slabs (which are also applicable to beams) are given in ACI 24.3. The intent of these requirements is to control flexural cracking: a larger number of fine cracks are preferable to a few wide cracks mainly for reasons of durability and ap-pearance.

A simple approach to address crack control in flexural mem-bers is given in ACI 24.3.2. The maximum center-to-center bar spacing s determined by the equations in ACI Table 24.3.2 for deformed bars is specifically meant to control cracking:

s =15 40,000f s

2.5cc 12 40,000f s

In this equation, fs is the calculated stress in the flexural rein-forcement closest to the tension face of the section caused by the service loads. Note that it is permitted to take fs equal to 2fy/3. The term cc is related to the clear cover of the reinforce-ment and is defined as the least distance from the surface of the reinforcement to the tension face of the member. For Grade 60 bars with cc 0.75 in. (minimum specified cover in ACI Table 20.6.1.3.1 for concrete that is not exposed to weather or in contact with the ground), the longitudinal reinforcing bars must be spaced no greater than 12 in. on center in order to satisfy crack control requirements. This value is generally less than the maximum spacing prescribed in ACI 7.7.2.3. Note that s is independent of the size of the flexural bars.

3.3.4 Minimum Spacing of Flexural Reinforcement

Spacing limits for nonprestressed reinforcing bars in a horizon-tal layer are given in ACI 25.2.1. In particular, the clear spacing between the bars must be at least the greatest of the follow-ing: 1 in., the diameter of the reinforcing bar, and (4/3) times the diameter of the largest aggregate in the concrete mix. These limits have been established primarily so that concrete can flow readily into the spaces between adjoining reinforcing bars and between reinforcing bars and formwork. Concrete must fully surround the reinforcing bars without honeycombing so that a good bond is established between the concrete and the steel.

3.3.5 Development of Longitudinal Reinforcement,

Flexural Cutoff Points, and Splices

Development of Flexural Reinforcement and

Cutoff Points

Flexural reinforcement must be properly developed or anchored in a one-way slab in order for it to perform as intended in accor-dance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in one-way slabs

are contained in ACI 7.7.3. Provided in these sections are required development lengths and termination locations for the flexural bars.

Development of flexural reinforcement must occur at the following critical sections in a one-way slab: (1) points of maxi-mum stress, that is, sections of maximum bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section.

In continuous one-way slabs subjected to uniform loads, the maximum positive and negative bending moments typically occur near the midspan and at the faces of the supports, respectively. Positive and negative flexural reinforcing bars must be developed or anchored on both sides of these criti-cal sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending mo-ment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that location as well.

Recommended flexural reinforcement details for one-way slabs are given in Fig. 3.2, which is adapted from Reference 7. The bar lengths in the figures are based on one-way slabs subjected to uniformly distributed gravity loads. Adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads. The bar lengths in these figures can also be used for one-way slabs that have been designed using the approximate bending moment coefficients given in ACI Table 6.5.2.

Splices

ACI 25.5 contains the requirements for lap splices, which, as noted in Section 1.3.3, are typically the most economical type of splice. Tension lap splices must be provided for flexural rein-forcement, and a consistent lap splice length should be speci-fied for a given bar size. Lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing.

Lap splice requirements for one-way slabs are essentially the same as those for beams (see Section 5.3.5 of this Guide for more information).




Fig. 4.1 Minimum Slab Thickness for Two-way Slabs without Interior Beams with Grade 60 Reinforcement.

Fig. 4.2 Preliminary Slab Thickness for Flat Plates.

CHAPTER 4 Two-way Slabs

4.1 OverviewGuidelines and recommendations on the economical design and detailing of two-way slabs are contained in this chapter. Information is provided on determining the thickness of the slab and detailing the reinforcement for the effects of flexure and shear. Specific requirements for two-way slab systems without beams that are part of the SFRS in structures as-signed to SDC C are given in Section 4.5.

4.2 Determining the Slab ThicknessThe first step in the design of a two-way slab system is to determine a preliminary slab thickness. A minimum slab thick-ness must be provided to control deflections and to provide adequate shear strength, where applicable.

Serviceability requirements for two-way slab systems with non-prestressed reinforcement are given in ACI 8.3.1. ACI Table 8.3.1.1 contains minimum thicknesses for two-way slabs without interior beams in systems without drop panels (flat plates) and with drop panels (two-way slabs). Also given in this table are minimum thick-nesses for these systems where exterior panels have an edge beam present and where they do not. Where beams are present on all sides of a panel, the minimum thickness is given in ACI Table 8.3.1.2. Figure 4.1 provides a summary of the minimum slab thick-ness requirements for two-way slabs without interior beams.

For two-way slab systems without beams, the minimum slab thickness that is required is often controlled by the two-way shear stresses that occur in the slab around the perimeter of the columns. Edge columns can be subjected to the largest shear stresses in the entire two-way system. Because two-way shear requirements are related to flexural requirements (the assumed distribution of shear stress around the critical section of a column includes the effects of unbalanced moments at a support), a slab thickness that satisfies both sets of requirements cannot be

obtained unless some simplifying assumptions are made. Figure 4.2, which is adapted from Reference 7, can be used to obtain a preliminary slab thickness for flat plates. The information in the figure is based on the following assumptions:

• Square edge column of size bending perpendicular to the slab edge with a three-sided critical section

• Column supporting a tributary area A

• Square bays

• Gravity load moment transferred between the slab and the edge column in accordance with the Direct Design Method requirement of ACI 8.10

• 4,000 psi normal-weight concrete




Fig. 4.3 Reinforcement Required at Corners of Slabs Supported by Stiff Edge Members.

Fig. 4.4 Alternative Reinforcement Layout at Corners of Slabs Supported by Stiff Edge Members.

The term qu is the total factored load, which must include an estimate of the slab weight; this weight can be estimated based on a slab thickness determined from the serviceability requirements. The ratio d/c1 is determined from Fig. 4.2 as a function of qu and the area ratio A/c12. A preliminary slab thickness h can be obtained by adding 1.25 in. to d acquired from the figure. The purpose of this design aid is to help de-crease the number of iterations that are needed to establish a viable slab thickness based on shear strength requirements; it is not meant to replace shear strength calculations.

It is common that the slab thickness determined based on strength and serviceability requirements will satisfy fire resis-tance requirements for typical residential and office occupan-cies. There is usually no need to increase the slab thickness to achieve a required fire rating in such cases.

The depth of the slab must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth based on serviceability and shear strength requirements. Specifying more than one slab depth results in formwork that is not economical.


4.3.1 Overview

Once the required area of flexural reinforcement has been determined in the column strips and middle strips for the factored bending moments along the span length using the strength design method, the size of reinforcing bars must be chosen to provide an area of steel that is greater than or equal to the amount that is required.

Additionally, minimum spacing between the flexural bars must be provided so that concrete can adequately flow in the voids between the bars. A maximum spacing between the flexural bars is required to limit the size the flexural crack widths. Finally, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corro-sive environments, to name a few.

The flexural reinforcement must be properly developed or anchored on both sides of a critical section. This ensures that the two-way slab will perform as intended in accordance with the strength design method.


Reinforcing bars are placed in a concrete member with a mini-mum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete members are given in ACI Table 20.6.1.3.1. Like in the case of one-way slabs, concrete cover is measured from the surface of the concrete to the outer edge of the longitudinal reinforcement for two-way slabs without stirrups.

Drip grooves or drip edges along the edge of a slab soffit can cause issues related to providing the required cover to the longitudinal reinforcement in two-way slabs. A discussion on

how to provide the required cover is given in Section 3.3.2 for one-way slabs, which is also applicable to two-way slabs.

4.3.3 Minimum and Maximum Bar Spacing

The minimum and maximum spacing of the flexural reinforce-ment in two-way slabs is given in ACI 8.7. As in the case of one-way slabs and beams, the minimum clear spacing is the greatest of 1 in., the diameter of the flexural bar, and (4/3) times the maximum aggregate size (ACI 25.2.1).

For nonprestressed solid slabs, the maximum center-to-center spacing of the flexural reinforcement is the lesser of 2 times the overall slab thickness and 18 in. This limitation helps con-trol cracking and provides for the possibility of loads concen-trated on small areas of the slab.

When selecting the size of the reinforcing bars, the largest bar size that will satisfy strength and serviceability requirements will usually provide overall economy. The spacing of the top bars should be limited to account for construction traffic. It is recommended that not less than #4 bars spaced at 12 in. on center be used to avoid displacement of the top bars.

4.3.4 Corner Reinforcement

ACI 8.7.3 addresses exterior corners of slabs that are sup-ported by stiff elements such as walls and edge beams. The presence of stiff elements restrains the lifting and causes additional bending moments at the exterior corners.

Corner reinforcement must be provided at both the top and the bottom of the slab, and the reinforcement in each layer in each direction must be designed for a bending moment equal to the largest positive bending moment per unit width in the slab panel. The top and bottom reinforcement must be placed parallel and perpendicular to the diagonal, respectively, as shown in Fig. 4.3 for a distance of at least one-fifth of the longer of the two span lengths in the corner panel. Reinforce-ment parallel to the edges is permitted to be used instead of the diagonal bars (see Fig. 4.4). This layout is preferred be-cause of ease in constructability compared to the other layout.




Fig. 4.5 Recommended Flexural Reinforcement Details for Two-way Slabs.




Cutoff Points

Flexural reinforcement must be properly developed or an-chored in a two-way slab in order for it to perform as intended in accordance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in column and middle strips of two-way slabs are contained in ACI 8.7.4. Provisions for required develop-ment lengths and termination locations for the flexural bars are given in that section.

Development of flexural reinforcement must occur at the fol-lowing critical sections in a two-way slab in both the column and middle strips: (1) points of maximum stress, that is, sec-tions of maximum bending moment and (2) locations where adjacent reinforcement is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section.

In continuous two-way slabs subjected to uniform loads, the maximum positive and negative bending moments in the column and middle strips typically occur near the midspan and at the faces of the supports, respectively. Positive and nega-tive flexural reinforcing bars must be developed or anchored on both sides of these critical sections. For cost savings, it is com-mon for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continuing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that loca-tion as well.

ACI Fig. 8.7.4.1.3a contains the minimum bar extensions in the column and middle strips in two-way slab systems without beams. These minimum lengths and extensions were devel-oped for uniformly distributed gravity loads only; adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads and/or lateral loads from wind or earthquakes.

The purpose of the structural integrity requirements of ACI 8.7.4.2 is to enable a two-way slab to span to adjacent sup-ports should a single intermediate support be damaged or destroyed. Two continuous column strip bottom bars through a support are provided to give the slab some residual strength after two-way shear failure at a single support.

Recommended flexural reinforcement details for two-way slabs subjected to uniform gravity loads are given in Fig. 4.5, which is adapted from Reference 7. Details for two-way slab systems without beams that are part of the SFRS are given in Section 4.5 of this Guide.

Lap Splices

ACI 25.5 contains the requirements for lap splices, which, as noted in Section 1.3.3, are typically the most economical type of splice. Tension lap splices must be provided for flexural rein-forcement, and a consistent lap splice length should be speci-fied for a given bar size. Lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing.

Lap splices requirements for two-way slabs are essentially the same as those for beams (see Section 5.3.5 of this Guide for more information).

4.3.6 Guidelines for Detailing the Flexural Reinforcement

The following guidelines are recommended when detailing the flexural reinforcement (Reference 8):

1. Layering. It is important to identify which reinforcing bars are to be placed in the outer layers and which are to be placed in the inner layers. It is common for the reinforcement in the direction of the larger design mo-ments be placed in the outer layers. A note or a section on the structural drawings can be provided to identify the inner and outer layers of flexural reinforcement.

2. Spacing. Reinforcing bars that are required in addition to the main, uniformly-spaced reinforcing bars in the column and middle strips should have a spacing that is a multiple of that provided for the main bars. These bars need to be clearly identified on the structural drawings.




Fig. 4.6 Placement of Reinforcement at Offset Columns.

Fig. 4.7 Placement of Slab Reinforcement at Column-line Beams.

Fig. 4.8 Openings in Slab Systems Without Beams (ACI 8.5.4).

3. Offset columns. Where columns are offset in plan, the top and bottom reinforcing bars should be placed orthogonally, if possible (see Fig. 4.6). This minimizes constructability issues compared to skewed bars. If skewed bars are required, they should be provided only in a separate, bottom layer; the top bars should be placed orthogonally. Top bars in the middle strip should be centered on a line connecting the column center lines.

4. Negative reinforcement at columns. In two-way slab systems without beams, the amount of negative rein-forcement at the columns may need to be increased above that required for pure flexure to satisfy the re-quirements in ACI 8.4.2 pertaining to the portion of the unbalanced moment transferred by flexure at the slab-column joint. This additional reinforcement needs to be clearly documented on the structural drawings. Where required, the additional bars are usually provided in the columns strip directly over the column while maintain-ing the typical bar spacing for the columns strip bars.

5. Beams. The location of the slab top reinforcement must be clearly indicated on the structural drawings where column-line beams are present. Because the minimum cover to the slab bars is smaller than that of the beam bars, the slab bars are typically placed above the top bars in the beam in the same plane as the beam stir-rups (see Fig. 4.7).

4.3.7 Openings in Slab Systems

ACI 8.5.4.1 permits openings of any size in two-way slab systems provided that an analysis of the system with the openings is performed that shows that all applicable strength and serviceability requirements of the Code are satisfied. For slabs without beams, such an analysis is waived when the provisions of ACI 8.5.4.2 are met. These provisions are illus-trated in Fig. 4.8, which is adapted from Reference 7.

The total area of reinforcement in a panel without an opening must be preserved in both directions of a panel with an open-ing. In other words, any reinforcement that is interrupted by an opening must be replaced on each side of the opening.

4.4 Detailing Requirements and Guide-lines for Shear Reinforcement

4.4.1 Overview

According to ACI 8.4.3 and 8.4.4, both one-way and two-way shear strength requirements must be satisfied for any two-way slab system supported directly on columns. One-way shear rarely governs; in most cases, two-way shear is more critical.




Fig. 4.9 Details for Closed Stirrup Shear Reinforcement in Two-way Slabs.

Fig. 4.10 Shear Studs at an Exterior Column used to Increase Punching Shear Capacity.

In cases where the two-way shear strength of the slab is not adequate and where other means to increase shear strength are not practical or feasible (for example, specifying a thicker slab or a larger column, introducing column-line beams, or providing drop panels or shear caps), it is permitted to supple-ment shear strength by providing one of the following types of reinforcement (see ACI Fig. R8.7.6(a)-(c)):

1. Single- or multiple-leg stirrups

2. Shearheads

3. Headed shear studs

Requirements for stirrups and headed shear studs are given in the following sections. Although once popular, shearheads and column capitals are rarely used anymore because they are not cost effective.

4.4.2 Single- or Multiple-leg Stirrups

Research has shown that the two-way shear strength of slabs can be increased by shear reinforcement consisting of prop-erly anchored single- or multiple-leg stirrups fabricated from bars or wires. The use of such reinforcement is permitted provided that the effective depth of the slab d is greater than 6 in. but not less than 16 times the bar diameter of the shear reinforcement (ACI 22.6.7.1).

Anchorage provisions for stirrups are given in ACI 25.7.1.3 for deformed reinforcing bars. For Grade 60 #5 stirrups and smaller and for Grade 40 #6 through #8 stirrups, anchorage is to be provided using a standard hook around the longitu-dinal reinforcement. For Grade 60 #6 through #8 stirrups the additional embedment length noted in that section must be provided in addition to the standard hooks. Table 5.4 in Section 5.4.3 of this Guide gives the minimum depth that is needed to develop Grade 60 #6 through #8 stirrups according to the provisions of ACI 25.7.1.3; it is evident from the table that these stirrups cannot be used in slabs of typical thickness that are found in buildings with typical occupancies.

Illustrated in Fig. 4.9, which is adapted from Reference 7, are required details for closed stirrup shear reinforcement in two-way slabs.

4.4.3 Headed Shear Studs

Tests have shown that shear reinforcement consisting of large headed studs welded to flat steel rails are effective in resisting two-way shear in slabs (see Fig. 4.10). Headed shear stud reinforcement can take the place of or can be used in conjunction with other means (drop panels, shear caps, etc.) to increase design shear strength. The base rail, which is set on chairs, is nailed to the formwork around the column. The size and spacing of the studs and the length of the base rail depends on the shear requirements.

Sufficient concrete cover must be provided to protect the base rail and head from weather, fire, and other effects. ACI 20.6.1.3.5 contains the minimum cover requirements for headed shear stud reinforcement. In particular, the concrete cover for the base rail and heads must not be less than that required for the reinforcement in the slab. ACI Fig. R20.6.1.3.5 illustrates these concrete cover requirements for headed shear stud reinforcement in slabs with both top and bottom bars

Illustrated in Fig. 4.11, which is adapted from Reference 7, are required details for headed shear stud reinforcement in two-way slabs.




Fig. 4.11 Details for Headed Shear Stud Reinforcement in Two-way Slabs. Fig. 4.12 Flexural Reinforcement Details for Two-way Slabs Without Beams in Structures Assigned to SDC C.

4.5 Detailing Requirements and Guide-lines for SDC C

Two-way slabs without beams are permitted to part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C; they are not permitted to be part of the SFRS in SDC D, E, or F.

All of the requirements and guidelines presented above are also applicable when such systems are part of the SFRS. In addition, the requirements in ACI 18.4.5 must be satisfied. Flexural reinforcement details based on these requirements are given in Fig. 4.12, which is adapted from Reference 7.




Beamside Form

BeamBottomPlyform

Plan View

Isometric

A B C

Fig. 5.1 Selecting a Beam Width for Formwork Economy.

CHAPTER 5 Beams

5.1 OverviewGuidelines and recommendations on the economical design and detailing of beams are contained in this chapter. Informa-tion is provided on sizing the cross-section and detailing the reinforcement for the effects due to flexure, shear, and torsion and combinations thereof. Specific requirements for beams in intermediate moment frames (SDC C) and special moment frames (SDC D, E, and F) are given in Sects. 5.7 and 5.8 of this Guide, respectively.

5.2 Sizing the Cross-section

5.2.1 Beam Depth

Establishing the dimensions of the cross-section is typically the initial step in the design of a reinforced concrete beam. The depth is usually determined first on the basis of deflec-tion requirements (see ACI Table 9.3.1.1 and Section 2.2.2 of this Guide). This depth sometimes needs to be modified for constructability, economy, or architectural reasons, to name a few.

It is important to consider economical formwork when choos-ing the depth of a beam. It is evident from ACI Table 9.3.1.1 that the minimum depth depends on the support conditions. For the usual case of continuous construction, the depth of the beam must be the same for all spans and it should be determined on the basis of the span that yields the largest minimum depth. More than one beam depth along the same line of beams results in formwork that is not economical. The same beam depth should be used not only throughout an entire floor/roof level but the entire structure as often as possible. In wide-module joist systems, the depth of the joists (beams) and the supporting beams (girders) must be the same for overall economy.

5.2.2 Beam Width

Once the overall depth of the beam has been established based on serviceability requirements and economy, the width of a beam can be determined by setting the design flexural strength Mn equal to the required flexural strength Mu for an assumed reinforcement ratio . Using the basic principles of the strength design method, the required width bw can be calculated by the following equation:

bw MuRnd

2

In this equation, 0.9 for tension-controlled sections, d distance from the extreme compression fiber to the centroid of the reinforcing steel, and Rn nominal strength coefficient of resistance, which can be determined by the following equation:

Rn f y 10.59 f y

fc'

Assuming f ’c 4,000 psi, fy 60,000 psi, and a reinforcement

ratio of approximately 50% of that corresponding to the reinforcement strain limit in ACI 9.3.3, the above equation for bw reduces to the following:

bw 20Mud 2

where Mu is in foot-kips and bw and d are in inches.

Providing a beam width that is equal to or greater than the value from this equation will result in cross-sectional dimen-sions that satisfy both strength and serviceability require-ments of ACI 318.

Because beams are part of a continuous floor and/or roof system, the largest factored bending moment Mu along the spans should be used in this equation. The beam width de-termined from the maximum Mu must be used for all spans; this will help in achieving economical formwork. Varying the amount of flexural reinforcement along the span lengths for different factored bending moments is by far more economi-cal than varying the beam width (or depth).

When selecting a beam width, it is also important to consider the width of the columns at the ends of the beam. Consider Cases A and B in Fig. 5.1. Greatest economy is achieved when the beam is as wide as or wider than the column: the form-work is much simpler compared to Case C where the beam is narrower than the column. Even though the formwork is sim-ple where the width of the beam is the same as the column, it is good practice to have a wider beam to avoid interference between the longitudinal corner bars of the beam and the column corner bars. It is recommended to have a beam width that is at least 4 in. wider than the column it frames into.




Fig. 5.2 Beam Sections Showing Drip Groove at Bottom Soffit: (a) Inad-equate Cover at Drip; (b) Shifting Reinforcing Cage to Maintain Adequate Cover at Drip Will Cause top Cover Problems; and (c) to Maintain Adequate Cover at all Locations, Stirrup Sizes may Need to be Changed. The Designer Must Consider the Effects of Shifting or Changing the Stirrups on Beam Capacity.

Fig. 5.3 Layering of Beam and Slab Reinforcing Bars can Create Sequencing Issues. Structural Drawings Should Designate Layer Locations and Concrete Covers.


5.3.1 Overview

Once the required area of flexural reinforcement has been determined for the factored bending moments along the span length using the strength design method, the number of reinforcing bars must be chosen to provide an area of steel that is equal to or greater than the amount that is required. It is important to ensure that the reinforcing bars will adequately fit within the cross-section of the beam.

In general, the minimum and maximum number of reinforc-ing bars in a single layer is a function of the cover and spacing requirements given in ACI 318-14. Minimum spacing between the longitudinal bars needs to be provided so that concrete can adequately flow in the voids between the bars. A maxi-mum spacing between the longitudinal bars is required to limit the size the flexural crack widths. Also, a minimum amount of concrete cover is needed to protect the bars from the effects of fire, weather, and corrosive environments, to name a few.

The longitudinal reinforcement must also be properly devel-oped or anchored on both sides of a critical section. This en-

sures the beam will perform as intended in accordance with the strength design method.


Concrete protection for reinforcement plays an important role in the formulation of the requirements of bar spacing and bar development. Reinforcing bars are placed in a concrete member with a minimum concrete cover to protect it from weather, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete construction are given in ACI Table 20.6.1.3.1. For beams that have transverse reinforcement in the form of stirrups that enclose the main flexural reinforcing bars, concrete cover is measured from the surface of the concrete to the outer edge of the stirrups.

A drip groove or edge in a beam soffit often times presents a problem in maintaining the required cover to the bars (see Reference 6 and Fig. 5.2a). It is not feasible to increase the concrete cover after the reinforcing bars in the beam have been detailed. Raising the stirrups from the bottom to achieve the required cover decreases the cover at the top (see Fig. 5.2b). The only practical solution is to measure the concrete cover from the drip groove and detail the stirrups accordingly, as shown in Fig. 5.2c. This will usually impact the overall depth of the beam and should be accounted for in design.

Maintaining the proper concrete cover can also be challenging at beam intersections. In particular, layering of the top steel in the slab at such intersections can create constructability issues. The sequencing and layering of beam and slab top reinforce-ment can also create serious congestions issues (see Fig. 5.3).

The following bar placing sequence is one way of avoiding the problems associated with this situation (see Reference 9):

1. Erect the reinforcement for the primary beams (bottom bars, stirrups, and top bars) as stand-alone cages and set in place.

2. Place the stirrups (bottom pieces of two-piece stirrups) and the bottom bars for the secondary beams.

3. Place the bottom bars for the slab (not depicted in Fig. 5.3 for clarity).

4. Place the top bars and the top pieces of the two-piece stirrups for the secondary beams.

5. Place the top bars for the slab.

5.3.3 Distribution of Flexural Reinforcement for

Crack Control

Requirements for the distribution of flexural reinforcement in beams (which are also applicable to one-way slabs; see Sec-tion 3.3.3 of this Guide) are given in ACI 24.3.

As discussed in Section 3.3.3, the maximum center-to-center bar spacing s determined by the equations in ACI Table 24.3.2 for deformed bars is as follows (see Fig. 5.4):

s =15 40,000f s

2.5cc 12 40,000f s




Fig. 5.4 – Maximum Spacing Requirements of Flexural Reinforcement.

Fig. 5.5 Spacing Limits of Flexural Reinforcement.

In this equation, fs is the calculated stress in the flexural reinforcement closest to the tension face of the section caused by the service loads. Note that it is permitted to take fs equal to 2fy /3. The term cc is related to the clear cover of the reinforcement and is defined as the least distance from the surface of the reinforcement to the tension face of the member. For Grade 60 bars with cc 2 in. (1.5 in. cover to a #4 stirrup), the longitudinal reinforcing bars must be spaced no greater than 10 in. on center in order to satisfy crack control requirements. Note that s is independent of the size of the flexural bars.

On the basis of the information given in Fig. 5.4 and the discussion above, the following equation provides the minimum number of bars nmin required in a single layer to control cracking:

nmin =bw 2 cc + 0.5db( )

s+1

The values of nmin determined by this equation should be rounded up to the next whole number. Note that a minimum of two bars are required to anchor the stirrups in beams.

The minimum number of bars can be tabulated for various beam widths, as shown in Table 5.1. The information in this table is based on the following:

• Grade 60 reinforcement

• Overall reinforcing bar diameter given in Table 2.1

• Least distance from the surface of the reinforcement to the tension face of the member cc 2 in.

• Calculated stress in the flexural reinforcement closest to the tension face of the section, caused by the service loads fs 40 ksi

Providing at least the number of flexural reinforcing bars in Table 5.1 for a given beam width automatically satisfies the crack control requirements of ACI 24.3.2.

Table 5.1 Minimum Number of Reinforcing Bars Required

in a Single Layer

Bar

SizeBeam Width (in.)

12 14 16 18 20 22 24 26 28 30 36 42 48

#4 2 2 3 3 3 3 3 4 4 4 5 5 6

#5 2 2 3 3 3 3 3 4 4 4 5 5 6

#6 2 2 3 3 3 3 3 4 4 4 5 5 6

#7 2 2 3 3 3 3 3 4 4 4 5 5 6

#8 2 2 3 3 3 3 3 4 4 4 5 5 6

#9 2 2 3 3 3 3 3 4 4 4 5 5 6

#10 2 2 3 3 3 3 3 4 4 4 5 5 6

#11 2 2 3 3 3 3 3 4 4 4 5 5 6

5.3.4 Minimum Spacing of Flexural Reinforcement

As noted in Section 3.3.4, spacing limits for reinforcing bars in a horizontal layer are given in ACI 25.2.1. The spacing require-ments are summarized in Fig. 5.5 for beams where dagg is the nominal maximum aggregate size in the concrete mixture. The following equation provides the maximum number of bars nmax that can fit in a single layer on the basis of the spacing requirements of ACI 25.2.1:

nmax =bw 2 cs + ds + r( )clear space( )+db

+1

Values of nmax determined by this equation should be rounded down to the next whole number.




Fig. 5.6 Recommended Flexural Reinforcement Details for Beams.

Table 5.2 contains the maximum number of bars that can fit in a single layer for various beam widths. The information in this table is based on the following:

• Grade 60 reinforcement.

• Clear cover to the stirrups cs 1.5 in. • Maximum aggregate size dagg 3/4 in.• #3 stirrups are used for #4 to #6 longitudinal bars, and #4

stirrups are used for #7 and larger longitudinal bars

Table 5.2 Maximum Number of Reinforcing Bars Permitted

in a Single Layer

Bar

SizeBeam Width (in.)

12 14 16 18 20 22 24 26 28 30 36 42 48

#4 5 6 7 8 10 11 12 14 15 16 20 24 28

#5 4 5 7 8 9 10 11 13 14 15 19 22 26

#6 4 5 6 7 8 9 10 11 12 14 17 20 23

#7 3 4 5 6 7 8 9 10 11 12 15 18 21

#8 3 4 5 6 7 7 8 9 10 11 14 16 19

#9 3 4 4 5 6 7 8 8 9 10 12 15 17

#10 2 3 4 5 5 6 7 7 8 9 11 13 15

#11 2 3 3 4 5 5 6 7 7 8 10 11 13

Selecting the number of bars within the limits of Tables 5.1 and 5.2 provides automatic conformity with the ACI 318 requirements for cover and spacing given the assumptions noted above. As discussed in Section 1.3.3, using the largest practical bar sizes that satisfy both strength and serviceability requirements results in overall cost savings.




Cutoff Points

Flexural reinforcement must be properly developed or an-chored in a concrete beam in order for the member to perform as intended in accordance with the strength design method. General requirements for development of reinforcement are given in ACI 25.4 and provisions for positive and negative flexural reinforcement in nonprestressed beams are contained in ACI 9.7.3. Provided in these sections are required develop-ment lengths and termination locations for the flexural bars.

Development of flexural reinforcement must occur at the following critical sections in a reinforced concrete beam: (1) points of maximum stress, that is, sections of maximum bending moment and (2) locations where adjacent reinforce-ment is terminated. Development length or anchorage of reinforcement is required on both sides of a critical section.

In continuous beams subjected to uniform loads, the maxi-mum positive and negative bending moments typically occur near the midspan and at the faces of the supports, respec-tively. Positive and negative flexural reinforcing bars must be

developed or anchored on both sides of these critical sections. For cost savings, it is common for some of the reinforcing bars to be terminated (or cut off) at locations away from the critical sections. For example, reinforcing bars are no longer required past a point of inflection on the bending moment diagram. Also, a portion of the bars can be theoretically cut off prior to the point of inflection at a location where the continu-ing bars are adequate to supply the required design strength. Because a critical section occurs at a cutoff point, the bars must be properly developed at that location as well.

Recommended flexural reinforcement details for reinforced concrete beams are given in Fig. 5.6, which is adapted from Reference 7. Included are the structural integrity requirements of ACI 9.7. The bar lengths in the figures are based on mem-bers subjected to uniformly distributed gravity loads. Adequate bar lengths must be determined by calculation for members subjected to the effects from other types of gravity loads and lateral loads. The bar lengths in these figures can also be used for members that have been designed using the approximate bending moment coefficients given in ACI Table 6.5.2.

Lap Splices

Splices of reinforcing bars are unavoidable in any reinforced concrete structure mostly because of transportation limitations. As noted in Section 2.2.3, lap splices are typically the most eco-nomical type of splice. ACI 25.5 contains the requirements for lap




Fig. 5.7 Contact and Noncontact Tension Lap Splices. Fig. 5.8 Two-legged U-stirrup.

splices. Tension lap splices must be provided for flexural reinforce-ment, and a consistent lap splice length should be specified for a given bar size. In a tension lap splice, the force in the reinforcing bars is transferred to the concrete by bond, which, in turn, trans-fers the force back to the adjacent reinforcing bars resulting in an essentially continuous line of reinforcement. As a result of this interaction, lap splice length is determined based on the concrete strength, the grade of the reinforcement, and the reinforcing bar size, location, and spacing.

There are two types of tension lap splices: contact lap splices and noncontact lap splices. The reinforcing bars in a contact lap splice touch and are wired together (see Fig. 5.7a). This type of splice is preferred because the bars are secured together and less likely to displace during construction compared to a noncontact lap splice where the bars do not touch (see Fig. 5.7b). There is a limit on how far the bars can be separated in a noncontact lap splice: the transverse center-to-center spacing of noncontact spliced bars must not exceed the lesser of one-fifth the required lap splice length and 6 in. (ACI 25.5.1.3).

Lap splice lengths of deformed bars in tension are given in ACI Table 25.5.2.1, and are a function of the tension development length of the bar d that is calculated in accordance with ACI 25.4.2.1(a). Class B tension splices are usually provided for beams.

Tension splices should be confined with transverse reinforce-ment, and if possible, located in zones of low tensile stresses (for example, near inflection points). This is intended to help prevent splice failure at the end of the splice due to splitting tensile stresses in the concrete. The location of a lap splice is different for top and bottom bars. For continuous top bars, lap splices generally occur away from the supports, which are typically the sections of maximum negative moment. Such splices are usually located within the middle third of the span length. Similarly, for bottom bars, the splices should occur near the supports.

Lapping of continuous bottom bars at supports often presents con-gestion and installation problems. Table 5.3, which is adapted from Reference 10, contains four splice arrangements for the bottom flexural bars along with their advantages and disadvantages based on constructability. In Arrangement No. 1, all of the bottom bars are spliced over the columns away from the section of maximum

positive moment, which is common. This arrangement can result in the most congestion in the beam-column joint. Arrangement No. 2 consists of half of the bottom bars spliced on one side of the joint and the other half on the other side of the joint, while Arrangement No. 3 has all of the splices located on one side of the joint. Finally, Arrangement No. 4 shows splice bars that pass through the joint, which are spliced to the bottom bars on both sides of the joint. Even though this arrangement increases the amount of steel that is required, the cost of the additional steel may be more than offset by the savings in labor and other costs, so it may be the most cost-effective arrangement in certain situations. In addition to constructa-bility, the appropriate splice arrangement must be chosen based on structural requirements for a particular situation.

5.4 Detailing Requirements and Guidelines for Shear Reinforcement

5.4.1 Overview

Shear reinforcement is provided in reinforced concrete beams to supplement the shear strength provided by the concrete. ACI 22.5.10 permits the following types of shear reinforcement:

1. Stirrups, ties, or hoops perpendicular to the longitudinal axis of the member

2. Welded wire reinforcement with wires located perpen-dicular to the longitudinal axis of the member

3. Spiral reinforcement

4. Inclined stirrups making an angle of at least 45 degrees with the longitudinal axis of the member and crossing the plane of the potential shear crack

5. Longitudinal reinforcement that is bent an angle of 30 degrees or more with respect to the longitudinal axis of the member

The most commonly used type of shear reinforcement in beams is stirrups that are oriented perpendicular to the axis of the member and are anchored to the longitudinal flexural reinforcement. The fol-lowing discussion focuses on this type of shear reinforcement.

5.4.2 Stirrup Configurations

Illustrated in Fig. 5.8 is a two-legged U-stirrup, which is com-monly utilized in reinforced concrete beams. Minimum inside bend diameters and standard hook geometry for stirrups are given in ACI Table 25.3.2.




Table 5.3 Splice Arrangement for Bottom Bars in a Reinforced Concrete Beam

Arrangement Advantages Disadvantages

1 BEAM

COLUMN

LAP LAP

Only continuous bottom bars are shown

• Simplest to detail

• Suitable arrangement where beams are wider than columns

• No additional reinforcing steel is required

• Can cause significant conges-tion, especially where the beam and column have the same width and/or where a large amount of continuous reinforce-ment is required

• Installation of single-bay preas-sembled beam cages is difficult

• Installation of multiple-bay preassembled cages is virtually impossible

2BEAM

COLUMN

LAP LAPLAP LAP


• Congestion is eased with no splices over the columns

• No additional reinforcing steel is required

• Detailing and preassembled cages are slightly more complex

• Preassembled beam cages are longer and more difficult to install

• Installation of multiple-bay preassembled cages is very difficult

3 BEAM

COLUMN

LAP LAP


• Detailing and preassembled cages are relatively simple

• Preassembled cages pass through only one joint, which make them easier to install than Arrangement No. 1 even though both arrangements have the same length

• No additional steel is required

• It is important to ensure that the cages are oriented correctly if installation begins at the cen-ter of the beam and progresses both ways

4 BEAM

COLUMN

LAP LAP LAP LAP


• No congestion at columns be-cause the splice bars that pass through the column are added later

• Preassembled cages are the shortest of all the arrangements

• The preassembled cages are very easy to install because no bottom bars pass through the column during installation

• Best arrangement for installation of multiple-bay preassembled cages

• Additional steel is required




Fig. 5.9 Beam Stirrup Configuration with Three Closed Stirrups Distributed Across the Beam Width.

Fig. 5.10 Alternate #1 Beam Stirrup Configuration.

Fig. 5.11 Alternate #2 Beam Stirrup Configuration.

In general, the size and spacing of the stirrups depends on the magnitude of the factored shear force at the section under consideration. It is common for the maximum shear force to occur at the supports and to decrease in magnitude to zero near midspan. An intricate stirrup layout closely following the variation in the shear diagram is not a cost-effective solution. Small stirrup sizes at a close spacing require disproportionate-ly high costs in labor for fabrication and placement. To achieve overall economy, larger stirrups at wider spacing (preferably the maximum spacing prescribed in ACI 318) should be provided, and the number of changes in the stirrup spacing along the span length should be kept to a minimum wherever practical.

As discussed in Section 5.2.2, beams should be wider than the columns that they frame in to. As floor systems become shallower, beams generally need to become wider. Proper stirrup detailing in wide beams is essential to ensure that the longitudinal flexural reinforcement and the stirrups are fully effective.

Research has shown that locating stirrups solely around the perimeter of a wide beam is not efficient where the beams are subjected to a relatively high shear demand (Reference 11). Stirrup legs are required in the interior of a wide beam. Illus-trated in Fig. 5.9 is a common stirrup configuration for a wide beam where three closed stirrups are provided. This configura-tion presents the following problems:

1. None of the stirrups traverse the full net width of the beam (the net width is defined as the gross width of the beam minus the required concrete cover on each side). Because of this, the overall width of the stirrup arrangement needs to be measured and verified in the field prior to installation. During installation, it is possible for the net width to change when the preas-sembled cage is hoisted into position by crane, which increases the risk that the provided cover will be less than that which is required.

2. If the stirrups are built in place instead of preassem-bled, the closed, one-piece stirrups make it difficult to place all of the required longitudinal reinforcement in the beam. It is especially difficult to place large, long longitudinal bars through the stirrups when stirrup top bars are present.

Two alternate stirrup configurations are illustrated in Figs. 5.10 and 5.11. In both configurations, a single, open stirrup is provided that extends the full net width of the beam. A stirrup cap consisting of a horizontal bar with a 135-degree hook at one end and a 90-degree hook at the other end is provided at the top of the configuration, which also extends the full net width of the beam. Providing a full-width stirrup helps in main-taining the correct concrete cover and facilitates installation of the beam reinforcement: the longitudinal bars can easily be placed within the beam from the top prior to installation of the stirrup cap.

The difference between the configurations in Figs. 5.10 and 5.11 occurs within the interior portion of the beam. In Fig. 5.10, two sets of identical U-stirrups with 135-degree hooks are shown symmetrically placed within the interior of the beam. Figure 5.11 shows one narrower U-stirrup nested inside a wider U-stirrup in the interior of the beam. Both of these configurations provide a cost-effective way of providing shear reinforcement for wide beams.

5.4.3 Development of Shear Reinforcement

Like in the case of flexural reinforcement, it is essential to properly develop and anchor shear reinforcement in order for it to be fully effective, that is, for it to develop its full yield strength. Requirements for the development of stirrups are given in ACI 25.7.1 and are illustrated in Fig. 5.12. Note that stirrups are to be provided as close to the tension and compression faces of the member as cover requirements and other reinforcement in the section permits.




• #5 stirrup bars and smaller• #6, #7 and #8 stirrup bars with fyt 40,000 psi

• #6, #7 and #8 stirrup bars with fyt 40,000 psi

Standard hook per ACI 25.3.2

h/2

h/2

Fig. 5.12 Anchorage Details for U-stirrups.

Fig. 5.13 Pair of U-Stirrups Forming a Closed Stirrup.

Each bend in the continuous portion of the U-stirrup must enclose a longitudinal bar and the ends of the stirrups must be anchored around the longitudinal bars using a standard hook defined in ACI 25.3.2 for #5 bar and smaller bars and #6 through #8 bars with fyt less than or equal to 40,000 psi. In addition to a standard hook, a minimum embedment length

equal to 0.014dbfyt / fc'( ) must be provided between the

outside edge of the hook and the mid-height of the member where #6, #7, or #8 stirrups with fyt greater than 40,000 psi are utilized. This additional anchorage requirement takes into consideration that (1) it is not possible to bend a #6, #7, or #8 stirrup tightly around a longitudinal bar, and (2) a large force can exist in the larger stirrup bars with fyt 40,000 psi.

The beam height that must be provided to satisfy the develop-ment requirements of ACI 25.7.2.3 is controlled by the size of the stirrup bar that is used. Minimum beam heights that sat-isfy these requirements are given in Table 5.4 for #6, #7, and #8 stirrup bars. The information that is provided in the table is based on the following:

• Normal-weight concrete

• Grade 60 reinforcement

• 1.5-in. cover to the stirrup hook

In short, #6, #7, and #8 stirrups are not permitted to be used in beams with heights less than those listed in the table.

Table 5.4 Minimum Beam Height to Accommodate #6, #7,

and #8 Stirrups of Grade 60 Reinforcement

Stirrup SizeBeam Height h (in.)

Concrete Compressive Strength f 'c (psi)

3,000 4,000 5,000 6,000

#6 26 23 21 20

#7 30 27 24 22

#8 34 30 27 25

Similarly, to allow for bend radii at corners of U stirrups, the minimum beam widths given in Table 5.5 must be provided.

Table 5.5 Minimum Beam Widths for Stirrup Development

Stirrup Size Beam Width bw (in.)

#3 10

#4 12

#5 14

#6 18

#7 20

#8 22

Provisions for closed stirrups formed from two U-stirrups are given in ACI 25.7.1.7. The legs of the stirrups must be lap spliced with a splice length of at least 1.3 d but not less than 12 in. where the tension development length d is determined in accordance with ACI 25.4.2 (see Fig. 5.13). In cases where the required lap length cannot fit within a member that has a height of at least 18 in., these stirrups can still be used, pro-vided that the force in each leg is equal to or less than 9,000 lb. Thus, for Grade 60 reinforcement, only a #3 stirrup satisfies this requirement (force in stirrup leg 0.11 60,000 6,600 lb).

5.5 Detailing Requirements and Guidelines for Torsional Reinforcement

5.5.1 Overview

Once a beam has cracked due to effects from a torsional mo-ment, its torsional resistance is provided primarily by closed stirrups and longitudinal bars. In beams subjected to torsion, shear, and bending moments, the amounts of transverse re-inforcement and longitudinal reinforcement required to resist all actions are determined using superposition (ACI 9.5.4.3). In other words, the required amounts of shear and torsion trans-verse reinforcement are added together as are the required amounts of flexural and torsional longitudinal reinforcement.

It is important to note that only the two legs of the stirrups that are adjacent to the sides of the beam are effective for tor-sion; stirrup legs within the interior of the beam can resist the effects from shear but not from torsion. This is consistent with the thin-walled tube methodology that forms the basis of the torsional provisions in ACI 318.




Fig. 5.14 Transverse Reinforcement Detail for Torsion Where Spalling is Restrained.

Fig. 5.15 Transverse Reinforcement Detail for Torsion Where Spalling is Not Restrained.

Fig. 5.16 Detailing Requirements for Longitudinal Torsional Reinforcement.

5.5.2 Detailing Requirements and Guidelines for the

Transverse Reinforcement

Diagonal cracks can form around all faces of a beam when it is subjected to a torsional moment in excess of that which causes cracking. Consequently, closed stirrups conforming to ACI 25.7.1.6 perpendicular to the axis of the beam must be provided.

It has been observed that the corners of beams subjected to torsion can spall off because of the inclined compressive stresses that occur at these locations. Thus, the transverse re-inforcement must be properly anchored so that it performs as intended. Because spalling is essentially prevented in beams with a slab on one or both sides of the web, ACI 25.7.1.6(b) permits the transverse reinforcement to be anchored by standard 90-degree hooks like in the case for shear anchorage (see Fig. 5.14). The 90-degree hook for the beam shown in this figure is located on the side that is adjacent to the slab, which restrains spalling.

ACI 25.7.1.6(a) requires that the transverse reinforcement be anchored by 135-degree hooks where spalling cannot be restrained (see Fig. 5.15). It has been observed that closed stirrups with 90-degree hooks fail when there is no restraint. Lapped U-stirrups, which are depicted in Fig. 5.13, are not

permitted in beams subjected to torsion because tests have shown that they are inadequate for resisting torsion due to a loss of bond when the concrete cover spalls.

The spacing of the transverse reinforcement is limited to the smaller of ph/8 and 12 in. where ph is equal to the perimeter of the centerline of the closed stirrups (ACI 9.7.6.3.3).

5.5.3 Detailing Requirements and Guidelines for the

Longitudinal Reinforcement

Longitudinal torsional reinforcement must be developed at both ends for tension. Proper bar anchorage is especially im-portant at the ends of a beam where high torsional moments commonly occur.

The following detailing requirements must be satisfied for longi-tudinal reinforcement for torsion (see Fig. 5.16 and ACI 9.7.5):

1. Longitudinal reinforcement must be distributed around the perimeter of the closed stirrups at a maximum spacing of 12 in.

2. At least one longitudinal bar is required in each corner of the stirrups.

3. The diameter of the longitudinal bars must be greater than or equal to 0.042 times the transverse reinforce-ment spacing, but not less than 3/8 in.

Torsional reinforcement must be provided for a distance that is greater than or equal to bt d beyond the point that it is theoretically required, where bt is the width of that part of the cross-section that contains the closed stirrups resisting torsion (ACI 9.7.5.3). This distance is larger than that used for shear reinforcement and flexural reinforcement because, as noted previously, torsional diagonal tension cracks develop in a helical form around a member.

5.5.4 Detailing Requirements and Guidelines for

Combined Effects

As was discussed in Section 5.5.1, for beams subjected to torsion, shear, and bending moments, the amounts of trans-verse reinforcement and longitudinal reinforcement required to resist all actions are determined using superposition. The




Top StepIn Beam

Bottom StepIn Beam Concrete Beam

Raised Floor System

Provide Min.Cover PerAci 318

≤ 3 in.

Additional BarsFor Crack Control

Increased CoverTo Main Bars

Optional Per Analysis

D1 D2

Provide Min.Cover PerAci 318

≤ 3 in.

2 in.

Bend Top Bars

Max. 1 To 6 Slope

Provide Additional StirrupsAt Each Bent Bar To ResistUpward Component Of BarTension (2 # 4 Min.)

Alternately, DrapeTop Bars

*

*

D1 D2

Fig. 5.17 Top and Bottom Steps in a Reinforced Concrete Beam.

Fig. 5.18 Reinforcement Details for a Reinforced Concrete Beam with a Top step Less Than or Equal to 3 in.

Fig. 5.19 Alternative Reinforcement Details for a Reinforced Concrete Beam with a Top Step Less Than or Equal to 3 in.

more restrictive of the provisions associated with these com-bined effects must be satisfied.

The following must be considered when detailing the rein-forcement for combined effects:

1. The most restrictive requirements for reinforcement spacing, cutoff points, and placement for torsion, shear, and flexure must be satisfied.

2. Negative and positive flexural reinforcement may be cutoff using the provisions of ACI 9.7.3 (see Section 5.3.5). When determining the theoretical cutoff points, the area of longitudinal torsional reinforcement must be subtracted from the total area of longitudinal reinforce-ment provided at that face.

3. The structural integrity requirements of ACI 9.7.7 must also be satisfied when detailing the reinforcement.

5.6 Steps in Beams

5.6.1 Overview

Steps in a reinforced concrete beam can occur for many reasons (Reference 12). For example, as shown in Fig. 5.17, the top of a beam would be needed to accommodate a raised flooring system. A bottom step in a beam would be required because of conflicts with mechanical equipment.

Ideal locations for steps would be at a column line or where support is provided by another beam. Obviously, it is not always possible to have the steps occur at these locations. The following sections provide detailing guidelines for steps of various depths.

5.6.2 Top Steps

Where the top step in a beam is 3 in. or less, the recommended detailing depends on when in the design and construction phases of the project the top step is introduced. In cases where the top step is known during the design phase, the beam can be designed for the smaller overall depth D1, which is illustrated in Fig. 5.18. The appropriate amounts of flexural and shear rein-forcement are provided for this reduced depth. Additional longitu-dinal bars are provided in the deeper section for crack control.

In cases where the step occurs after the design is complete, additional flexural and shear reinforcement may be required compared to the original design because of the reduced beam depth. Both flexural and shear strength need to be checked and the corresponding longitudinal bars and stirrups may have to be adjusted accordingly.

A top step introduced late in the design phase or early in the construction phase can be accommodated using bent top reinforcement as illustrated in Fig. 5.19. ACI 10.7.4.1 limits the slope of the inclined portion of the offset bent longitudinal bars to 1 in 6 relative to the longitudinal axis of the beam. Additional stirrups need to be provided in the beam at this location to resist the upward component of the tensile force in the longitudinal bars. Two #4 bars are commonly provided at bent bar locations.

In lieu of using the bent bar configuration illustrated in Fig. 5.19, either the top bars can be draped or the top reinforce-ment on either side of the step can be spliced using a noncon-tact lap splice provided the spacing limitations of ACI 25.5.1.3 can be satisfied.

In cases where top steps exceed 3 in., the recommended de-tail depends on where along the length of the beam the step occurs. If the step occurs near midspan or at other sections where the force in the top reinforcement is relatively low, the top bars of the shallower beam can extend into the deeper beam a distance equal to the development length of these bars (see Fig. 5.20). The top bars of the deeper section can be hooked at the location of the step as illustrated in the figure.

If the step occurs near a support or at other sections where the force in the top bars are relatively high, structural design




> 3 in.

Cover PerACI 318

Provide Additional StirrupsAs Required Per Design

90° Hook

Development Length When Top Steel Is Not In TensionClass 'B' Splice When Top Steel Is In Tension

Splice *D1

D2

*

Fig. 5.20 Reinforcement Details for a Reinforced Concrete Beam with a Top Step Greater than 3 in.

Fig. 5.21 Reinforcement Details for a Reinforced Concrete Beam with a Top Step at a Column.

Fig. 5.22 Reinforcement Details for a Reinforced Concrete Beam with a Bottom Step at a Column.

Fig. 5.23 Reinforcement Details for a Reinforced Concrete Beam with a Deep Step.

Top Bars HookedOr Developed IntoBeam

Standard 90° Hook

Column

D1

D2

Additional StirrupsAs Required (Typ.)

If Possible Extend The BeamAnd Bottom ReinforcementTo Support

Class 'B'

D1

Greater OfD1 Or D2

Splice (Min.)D2

Rigid BentDiagonal Bars As Required

Shear StirrupsAs Required

Standard 90° Hook

Beam

Step

D1

D2

Ldh Min.

D1, D2, OrLdh + Cover

Greater Of

of the reinforcement is required using conventional or strut-and-tie methods. It is good practice to extend the top bars of the shallower beam at least a Class B splice length into the deeper beam (Note: technically this is not a lap splice because the spacing requirements of ACI 25.5.1.3 are not satisfied).

Additional stirrups may be required at the location of the step to resist the reaction of the shallower beam into the deeper beam. The amount and spacing depends on the shear demand at this section.

As noted previously, the ideal location for a top step occurs where a beam frames into another beam or into a column. Illustrated in Fig. 5.21 are recommended details where the step occurs at a column. The top bars of the shallower beam can be either hooked or extended a development length into the deeper beam.

5.6.3 Bottom Steps

The reinforcement details illustrated in Fig. 5.22 can be used where a bottom step in a beam is located near a column. The length of the intersecting beam segment should be at least equal to the depth of the deeper member to ensure that a 45-degree strut can form within this region.

5.6.4 Deep Steps

Illustrated in Fig. 5.23 are recommended details for beams with deep steps, that is, steps that exceed the depth of the beam. It is good practice to have the width of the bent greater than or equal to the depths of the adjacent beams.

5.7 Detailing Requirements and Guidelines for SDC C

5.7.1 Overview

The requirements in ACI 18.4.2 must be satisfied for beams that are part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C. All of the re-quirements and guidelines presented above are also applicable.

5.7.2 Design for Flexure

ACI 18.4.2.2 requires that the minimum positive moment strength at the faces of the supports be equal to at least 33% of the nega-tive moment strength at that joint. This allows for the possibility that the positive moment caused by earthquake-induced lateral displacements exceeds the negative moment due to gravity loads. Similarly, the minimum negative and positive moment strength at any section along the span of the beam must be equal to at least 20% of the maximum moment strength at either joint.




Fig. 5.24 Flexural requirements for beams in intermediate moment frames.

Fig. 5.25 Examples of Hoops and Overlapping Hoops.

Fig. 5.26 Transverse Reinforcement Requirements for Beams in Intermediate Moment Frames.

A summary of the flexural requirements for beams in interme-diate moment frames is given in Fig. 5.24, which is adapted from Reference 7.

ACI 18.4.2.2 does not contain any restrictions on where lap splices of the flexural reinforcement can be located along the span. As noted in Section 5.3.5, top reinforcement is spliced near midspan and bottom reinforcement is spliced near the ends. However, because the potential exists for plastic hinges to form at the ends of the beam, it would be appropriate to locate the splices of the bottom bars somewhere between the ends of the beam and midspan.

5.7.3 Design for Shear

ACI 18.4.2.3 contains two methods on how to determine the maximum shear force on a beam in an intermediate moment frame. In the first method, the maximum factored shear force is obtained from the factored gravity loads acting on the beam plus the shear force associated with the application of the nominal moment strength Mn at each end of the beam. Both sidesway to the right and to left must be considered. In the second method, the maximum shear force is obtained from the design load combinations that include earthquake effects E, where E is assumed to be twice that prescribed by the building code. It is permitted to design for not less than the smaller of the two shear forces obtained from these methods.

The required shear reinforcement is obtained from the maximum shear force described above. Because the shear reinforcement depends on Mn, it is important not to need-lessly provide more flexural reinforcement than required because that can have a direct impact on the amount of shear reinforcement that has to be provided.

Within a distance of at least 2h from the face of each support, hoops must be provided to resist the required shear force. A hoop is defined as a closed tie or continuously wound tie that is made up of one or several reinforcement elements, each having seismic hooks that conform to ACI 25.3.4 at both

ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement elements in hoops must engage a longitudinal bar in the beam (ACI 25.7.4.2). Examples of hoops and overlapping hoops are illustrated in Fig. 5.25, which is adapted from Reference 7. As discussed in Section 5.4.2, hoops made from Details B and C make placement of the longitudinal bars in the beam much easier than those using Detail A.




Fig. 5.27 Dimensional Limits of Beams in Special Moment Frames.Fig. 5.28 Flexural Requirements for Beams in Special Moment Frames.

Fig. 5.29 Lap Splice Requirements for Beams in Special Moment Frames.

Once the required size and spacing of the hoops are determined, the spacing must be checked against the minimum spacing requirements of ACI 18.4.2.4. Outside of the regions where hoops are required, stirrups may be used; these stirrups must be provided over that entire region. Figure 5.26, which is adapted from Reference 7, illustrates the transverse reinforcement require-ments for beams in intermediate moment frames.

5.8 Detailing Requirements and Guidelines for SDC D, E, or F

5.8.1 Overview

The requirements in ACI 18.6 must be satisfied for beams that are part of a special moment frame, which is the required SFRS for buildings assigned to SDC D, E, or F. All of the requirements and guidelines presented above are also applicable.

5.8.2 Dimensional Limits

Dimensional limits for beams in special moment frames are given in ACI 18.6.2.1. These limits have been guided by ex-perimental evidence and observations of reinforced concrete frames that have performed well in the past during an earth-quake. A summary of these limits is given in Fig. 5.27, which is adapted from Reference 7. It is important that these limits are satisfied once the beam dimensions have been initially established using the information in Section 5.2 of this Guide.

5.8.3 Design for Flexure

ACI 18.6.3 requires that the minimum positive moment strength at the faces of the supports be equal to at least 50% of the nega-tive moment strength at that joint. This allows for the possibility that the positive moment caused by earthquake-induced lateral displacements exceeds the negative moment due to gravity

loads. Similarly, the minimum negative and positive moment strength at any section along the span of the beam must be equal to at least 25% of the maximum moment strength at either joint.

A summary of the flexural requirements for beams in special moment frames is given in Fig. 5.28, which is adapted from Reference 7. It is usually best to specify a smaller number of larger longitudinal bars to help reduce congestion at the beam-column joints.

ACI 18.6.3.3 contains specific requirements for lap splice locations in beams of special moment frames. Lap splices are permitted as long as they are properly confined with hoop or spiral reinforcement over the entire lap length and that they are located away from potential hinge areas at the ends of the beam. Provisions for lap splices are illustrated in Fig. 5.29, which is adapted from Reference 7.

5.8.4 Design for Shear

Shear design for beams in a special moment frame is related to the maximum flexural strength that can be developed in the




Fig. 5.30 Transverse Reinforcement Requirements for Beams in Special Moment Frames.

Fig. 5.31 Requirements of ACI 18.14.3.2(a) for Beams.

Fig. 5.32 Requirements of ACI 18.14.3.3 for Beams.

beam, which is defined in ACI 18.6.5.1 as the probable flexural strength Mpr. The maximum factored shear force is obtained from the factored gravity loads acting on the beam plus the shear force associated with the application of the probable flexural strength Mpr at each end of the beam. Both sidesway to the right and to the left must be considered.

The required shear reinforcement is obtained from the maxi-mum shear force described above. Because the shear rein-forcement depends on Mpr , which is a function of the amount of flexural reinforcement in the section, it is important not to needlessly provide more flexural reinforcement than required because that can have a direct impact on the amount of shear reinforcement that has to be provided.

According to ACI 18.6.4.2, the spacing between longitudinal bars that are restrained by legs of crossties or hoops is limited to 14 in. This provision helps to ensure that proper lateral support is provided for such bars in case they are subjected to compressive forces under moment reversals.

Within a distance of at least 2h from the face of each support, hoops must be provided to resist the required shear force. A hoop is defined as a closed tie or continuously wound tie that is made up of one or several reinforcement elements, each having seismic hooks that conform to ACI 25.3.4 at both ends (ACI 2.3 and 25.7.4.1). The ends of the reinforcement elements in hoops must engage a longitudinal bar in the beam (ACI 25.7.4.2). Examples of hoops and overlapping hoops are illustrated in Fig. 5.25, which is adapted from Reference 7. As discussed in Section 5.4.2, hoops made from Details B and C make placement of the longitudinal bars in the beam much easier than those from Detail A.

Once the required size and spacing of the hoops are determined, the spacing must be checked against the maximum spacing re-quirements of ACI 18.6.4.4. Outside of the regions where hoops are required, stirrups with seismic hooks may be used; these stir-rups must be provided over that entire region. Figure 5.30, which is adapted from Reference 7, illustrates the transverse reinforce-ment requirements for beams in special moment frames.

5.9 Beams Not Designated as Part of the SFRS

Detailing requirements for beams that have not been assigned to the SFRS are given in ACI 18.14.3.

In cases where the bending moments and shear forces in a beam due to the lateral displacements from a seismic event do not exceed the design moment and shear strength of the beam, the detailing requirements of ACI 18.14.3.2(a) must be satisfied. These requirements are illustrated in Fig. 5.31, which is adapted from Reference 7.

Where the induced bending and shear exceed the design mo-ment and shear strength of the beam, or where the induced moments and shear are not calculated, the detailing require-ments of ACI 18.14.3.3 must be satisfied (see Fig. 5.32, which is adapted from Reference 7).




Fig. 6.1 Preliminary Sizing Chart for Nonslender Columns with Tie Reinforcement.

CHAPTER 6 Columns

6.1 OverviewGuidelines and recommendations on the economical design and detailing of columns are contained in this chapter. Infor-mation is provided on sizing the cross-section and detailing the longitudinal and transverse reinforcement. Specific re-quirements for columns in intermediate moment frames (SDC C) and special moment frames (SDC D, E, and F) are given in Sects. 6.6 and 6.7 of this Guide, respectively.

6.2 Preliminary Column SizingThe preliminary size of a typical column in a reinforced concrete building is needed for a variety of reasons, includ-ing frame analysis and initial cost estimation. It is common practice to obtain preliminary column sizes in the early stages of design utilizing axial gravity loads only. It is assumed that the effects from bending moments are relatively small and that slenderness (secondary) effects are negligible. The first of these assumptions is usually valid for columns that are not part of the lateral force-resisting system. For many columns, slenderness effects are not an issue.

A preliminary column size can be obtained by setting the total fac-tored axial load Pu equal to the design axial load strength Pn,max given in ACI Table 22.4.2.1 for columns with ties conforming to ACI 22.4.2.4 and with spirals conforming to ACI 22.4.2.5. The appropriate equation is solved for the gross area of the column Ag, assuming practical values for the total area of longitudinal reinforcement Ast, the compressive strength of the concrete f '

c, and the yield strength of the longitudinal reinforcement :

Tied Column: Ag Pu /0.80[(0.85)f 'c ) fy ]

Spiral Column: Ag Pu/0.85[(0.85)f 'c ) fy ]

where Ast /Ag.

The minimum and maximum areas of longitudinal reinforce-ment are prescribed in ACI 10.6.1.1. The following limits are applicable regardless of the type of transverse reinforcement that is used in the column:

• Minimum Ast 0.01Ag• Maximum Ast 0.08Ag

The 1% lower limit is meant to provide resistance to any bending moments that are not accounted for in the analysis because of, for example, construction tolerances or misalign-ments. This lower limit is also meant to help reduce creep and shrinkage in the concrete under sustained compressive stresses. In order for the concrete to be properly placed and consolidated, the size and number of longitudinal reinforcing bars must be chosen to minimize reinforcement congestion (see Section 6.3 of this Guide). The upper limit on the longitu-dinal reinforcement is meant to help achieve these goals. The maximum area of reinforcement must not exceed 4% of the gross column area at sections where lap splices are utilized.

A preliminary column size should be determined using a low percentage of longitudinal reinforcement. Columns that have longitudinal reinforcement ratios Ast /Ag in the range of 1 to 2% are usually the most economical because concrete carries axial compressive loads more cost-effectively than reinforcing steel. Generally, it is usually more economical to use larger column sizes with less longitudinal reinforcement.

The information contained in Fig. 6.1, which is adapted from Reference 7, can be used to obtain a preliminary size of a non-slender, tied column with Grade 60 longitudinal reinforcement. The chart can be entered with a longitudinal reinforcement ratio and concrete compressive strength; the ratio of factored axial force Pu to gross area of the column Ag can be read from the vertical axis, which can be solved for Ag. Similar design charts can be generated for other column sizes and shapes and other material strengths.

As noted in Section 2.2.2 of this Guide, the same column size should be used as often as possible throughout the entire building to achieve overall economy. The dimensions of a col-umn can be influenced by architectural and functional require-ments. One or both dimensions of a rectangular column may be limited, which could result in a column that is slender.

A number of design aids are available that can be utilized in the design of columns subjected to axial load and bending moment. Reference 13 contains nondimensionalized nominal strength interaction diagrams for rectangular and circular sec-tions with a variety of bar arrangements. Numerous tables for rectangular and circular columns are contained in Reference 14, which cover a wide range of cross-sectional dimensions,




concrete compressive strength, longitudinal reinforcement ratios, and bar arrangements. These tables contain values cor-responding to key points on the interaction diagram.

6.3 Detailing Requirements and Guide-lines for Longitudinal Reinforcement

6.3.1 Overview

Longitudinal reinforcement for columns must satisfy the requirements in ACI 10.7. Limitations are provided on the size and spacing of the longitudinal bars.

The longitudinal bars must be spaced far enough apart so that concrete can flow easily between the bars. Minimum bar spacing is especially critical at splice locations. Generally, it is more economical to have a fewer number of larger longitudi-nal bars than a greater number of smaller bars.

Splice requirements for longitudinal reinforcement in columns are given in ACI 10.7.5. The type of lap splice that must be provided is based on the stress in the reinforcing bars under factored loads.

6.3.2 Minimum Number of Longitudinal Bars

According to ACI 10.7.3.1, a minimum of four longitudinal bars are required in columns where rectangular or circular ties are used as transverse reinforcement. For columns where the longitudinal reinforcement is enclosed by spirals, a minimum of six longitudinal bars are required.

For other tie shapes, one bar should be provided at each apex or corner and proper transverse reinforcement provided. For example, a tied triangular column needs three longitudinal bars, with one at each apex of the triangular ties.

6.3.3 Spacing of Longitudinal Bars

The longitudinal bars in reinforced concrete columns must be spaced at a sufficient distance so that concrete can flow eas-ily between the bars and between the bars and the formwork. According to ACI 25.2.3 the minimum clear distance that is to be provided between longitudinal bars is equal to the largest of the following:

• 1.5 times the diameter of the longitudinal bar

• 1.5 in.

• (4/3) times the diameter of the largest aggregate in the concrete mix

These minimum clear distance requirements are also appli-cable to the clear distance between a contact lap splice and any adjacent bars or splices.

Table 6.1, which is adapted from Reference 7, contains the minimum face dimension of rectangular tied columns with normal lap splices based on the requirements presented above. The column face dimensions have been rounded to the nearest inch and a 1.5-in. clear cover to #4 ties has been used.

The maximum number of bars in a circular or square column that has longitudinal bars arranged in a circle with normal lap

Table 6.1 Minimum Face Dimension (inches) of

Rectangular Tied Columns with Normal Lap Splices.

Bar

Size

Number of Bar Per Face

2 3 4 5 6 7 8 9 10 11 12 13 14

#5 8 10 12 14 17 19 21 23 25 27 29 31 34

#6 9 11 13 15 18 20 22 24 27 29 31 33 36

#7 9 11 14 16 18 21 23 26 28 30 33 35 37

#8 9 12 14 17 19 22 24 27 29 32 34 37 39

#9 10 13 16 18 21 24 26 30 33 35 38 41 44

#10 11 14 17 20 23 27 30 33 36 39 42 46 49

#11 11 15 18 22 25 29 32 36 40 43 47 50 54

Table 6.2 Maximum Number of Bars in Columns

Having Longitudinal Bars Arranged in a Circle and

Normal Lap Splices.

h

(in.)

Bar Size

#5 #6 #7 #8 #9 #10 #11

12 8 7 6 6 4* — —

14 11 10 9 8 7 5* 4*

16 14 13 12 11 9 7 6

18 17 16 14 13 11 9 8

20 20 19 17 16 13 11 10

22 23 21 20 18 16 13 12

24 26 24 22 21 18 15 13

26 29 27 25 23 20 17 15

28 32 30 28 26 22 19 17

30 35 33 30 28 25 21 19

32 38 35 33 31 27 23 21

34 41 38 36 33 29 25 22

36 44 41 38 36 31 27 24

* Applicable to circular tied columns only




Fig. 6.2 Tie and Splice Details in a Reinforced Concrete Column.

splices is contained in Table 6.2, which is also adapted from Reference 7. The information given in this figure satisfies the minimum clear distance requirements of ACI 25.2 and the reinforcement limits of ACI 10.6.1.1. The number of bars have been rounded to the nearest whole number and were deter-mined using a 1.5-in clear cover to #4 spirals or ties.

6.3.4 Splices

Provisions for lap splices, mechanical splices, butt-welded splices, and end-bearing splices are given in ACI 10.7.5. In general, column splices must satisfy the requirements for all load combinations. Where the longitudinal bar stress due to factored loads is compressive, all of the splice types listed above may be used. Lap splices and mechanical or butt-weld-ed splices are permitted when the longitudinal bar stress is tensile; end-bearing splices are not permitted in such cases.

Lap splices are the most popular and usually the most economical type of splices used in columns. The type of lap splice—compressive or tensile—that must be used depends on the stress in the longitudinal bars due to the factored load combinations. Lap splices in columns that are not part of spe-cial moment frames are permitted to occur immediately above the top of the slab, as shown in Fig. 6.2. This location facili-

tates the overall construction of the structure. The longitudinal bars from the column below extend above the slab a distance equal to or greater than the required lap splice length.

It is common to have construction documents that show lap splices occurring at each floor level. Depending on a number of factors, the tension lap splice lengths may be relatively long, in some cases close to the entire story height. This results in doubling of the longitudinal bars, which may cause congestion in the column and make concrete placement more difficult. As a general rule, if the lap splice length is more than about one-third to one-half the story height, it may be more economical to splice the bars every other floor, if possible. Additional information on lap splice location and guidelines on constructability can be found in Reference 15.

At lap splice locations or at locations where the column size changes, offset bends conforming to ACI 10.7.4 are required (see Fig. 6.4). It is standard construction practice for the lon-gitudinal bars in the column below to be offset bent into the column above. From a construction perspective, it is easier to lower the larger column cage over the smaller offset cage that protrudes from the floor slab.

6.4 Detailing Requirements and Guide-lines for Transverse Reinforcement

6.4.1 Overview

Transverse reinforcement for columns must satisfy the require-ments given in ACI 10.7. Limitations are provided on the size and spacing of both tie and spiral transverse reinforcement.

The transverse bars must be spaced far enough apart so that concrete can flow easily between the bars without honeycomb-ing. Additionally, these bars must be spaced close enough to provide adequate lateral support to the longitudinal reinforce-ment and to provide sufficient shear strength where needed.

6.4.2 Spiral Reinforcement

Requirements for columns with spiral reinforcement are given in ACI 10.7.6 and 25.7.3. Standard spiral sizes are #3 to #5, and the clear spacing between spirals should not exceed 3 in. or be less than the greater of 1 in. or (4/3) times the diameter of the largest aggregate in the concrete mix.

ACI Eq. (25.7.3.3) is to be used to determine the minimum amount of spiral reinforcement that must be provided:

s = 0.45AgAch

1 fc'

f yt

The volumetric spiral reinforcement ratio is equal to the volume of the spiral reinforcement divided by the volume of the concrete core measured to the outside edges of the spiral reinforcement. The term Ach is the area of the column core enclosed by the spiral, which is equal to Dch)2/4 where Dch is the diameter of the column core measured to the outside edges of the spiral reinforcement (see Fig. 6.3, which is adapted from Reference 7).




Fig. 6.3 Spiral Reinforcement.

Fig. 6.4 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection.

Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) “B” indicates bundled bars. Bundles shall not exceed four bars; and 4) elimination of tie for center bar in groups of three limits clear spacing to be 6 in. maximum. Unless otherwise specified, bars should be so grouped.

Thus, for a given spiral bar with an area of Abs, the center-to-center spacing of the spirals s (i.e., the pitch) must be less than or equal to the value obtained by the following equation:

s = 8.9AbsDch Ag /Ach( ) 1 fc

' /fyt( )

Spiral reinforcement provides a higher degree of lateral con-finement than that provided by ties; this has a direct impact on the design strength of a column. This is reflected in the larger strength reduction factor that is permitted to be used in the design of a spiral column compared to that in a tied column. One drawback of spiral reinforce-ment occurs at beam-column joints: it may be difficult to thread the longitudinal bars of the beam through the joint, espe-cially where the pitch is relatively small.

6.4.3 Tie Reinforcement

Requirements for columns with tie reinforcement are given in ACI 10.7.6 and 25.7.2. Standard hook dimensions for ties, which are the same as those for stirrups, are given in ACI 25.3.2. Maximum tie spacing and other requirements are illus-trated in Fig. 6.4 (Reference 16).

Illustrated in ACI Fig. R25.7.2.3(a) are the requirements of ACI 25.7.2.3 pertaining to tie arrangement and maximum clear spacing between laterally supported bars. The corner bars and every other longi-tudinal bar must have lateral support in cases where the center-to-center spacing of the longitudinal bars on a side is equal to or less than 6 in. plus the diameter of the longitudinal bar. Additional lateral support for the intermediate bars must also be provided if the spacing is greater than that. This is usually in the form of a crosstie (sometimes referred to as a candy cane because of its shape), which is a reinforcing bar that has a seismic hook on one end and a hook not less than 90 degrees with at least a six-diameter extension on the other. A seismic hook is defined as a hook with a bend that is not less than 135 degrees and an exten-sion that is not less than 6 bar diameters or 3 in., whichever is greater. For circular hoops, the bend should not be less than 90 degrees.

Standard arrangements of column ties are depicted in Figs. 6.4 and 6.5. The one-piece tie arrangements in Fig. 6.4 are sufficiently rigid to be lifted into place after being preassembled on site. If possible,




Fig. 6.5 Standard Column Ties Applicable for Either Preassembled Cages or Field Erection, Special-shaped Columns, and Columns with Bars in Two Faces Only.

Notes: 1) Alternate position of hooks in placing successive sets of ties; 2) minimum lap shall be 12 in.; 3) elimination of tie for center bar in groups of three limits clear spacing to be 6 in. maximum. Unless otherwise specified, bars should be so grouped; and 7) bars shown as open circles may be accommodated provided clear spaces between bars do not exceed 6 in. (Figure does not include Notes 3-6.)

(a)

(b)

(a)

(b)

(c)Fig. 6.6 Column Tie Sets Comprising Multiple Ties: (a) With Outer Confinement Tie and Inner Closed Tie; (b) With Outer Confinement Tie and Candy Cane Ties; and (c) With Paired Overlapping Ties.

Fig. 6.7 Column Tie Configurations Using Multiple Bars: (a) Diamond Tie (avoid use); and (b) Single Closed Tie with Candy Cane Ties.

it is preferred to preassemble one-story column cages where all of the lap splices occur at or near the same elevation above the floor line.

There are numerous ways to arrange ties in a col-umn and some arrangements are preferred more than others. For example, consider the arrange-ments in Fig. 6.6a and 6.6b, which consist of an outer confinement tie with an inner tie and cross-ties, respectively. These arrangements are gener-ally preferred over the arrangement in Fig. 6.6c, which consists of paired overlapping ties, because of the following (Reference 16):

• The outer confinement tie acts as a template for the ironworker to place the longitudinal bars in the column.

• It is easier to maintain the required concrete cover using side-form spacers.

• It is more efficient at preventing displacement of the longitudinal bars while the column cage is being moved into place by crane.

• The tasks that are needed to be completed by the ironworker are simplified, which translates to increased productivity.

One exception to using outer confinement ties is where a column is dimensionally large. In such cases, the arrangement in Fig. 6.6c is preferred so as to avoid difficulties associated with fabricating, shipping, and placing the ties.

Generally, crossties (Fig. 6.6b) are preferred over closed ties (Fig. 6.6a) because the latter are difficult to place and align around the longitudinal bars. Crossties can easily be placed after the column cage has been constructed with the outer confine-ment ties.

The diamond ties depicted in Fig. 6.7 are difficult to fabricate and difficult to place and align around the longitudinal bars in the column. Crossties should be used instead, which facilitates bar placement and allows more accurate column cage fabrication.

Illustrated in Fig. 6.8 are examples of tie arrange-ments where precise fabricating dimensions are difficult to maintain and where the fabricated pieces are costly to place (Reference 16). The alter-nate details are more efficient and economical for the reasons stated in the figure.




TIES FOR 12 BAR COLUMN


Problem: Any out of location placement of the 10 bars

will affect the others

Initial Detail Suggested Alternate Detail


ALTERNATEHOOKS (TYP.)

Problem: Out of location placement of any bars will affect the others

Advantage: Bars are less dependent on location of others




SMALL DIAMETER (12” OR LESS) CIRCULAR COLUMNSUSING #3 OR #4 TIES

Problem: Small circle (Bend Type T3) is difficultto bend and keep in the same plane

Advantage: More accurate and better alignment of bars


Problem: Any out of location placement of the 12 bars

will affect the others


Initial Detail


Suggested Alternate Detail

Fig. 6.8 Costly and Economical Column Tie Configurations.




Fig. 6.9 Column and Footing Detail: (a) as shown in construction documents; and (b) as detailed for constructibility, with dowels supported on the footing reinforcing bars and straight column bars (no offsets).

(a)

(b)

(c)

Fig. 6.10 (a) Ideal Arrangement of Dowels (b) Dowels Arranged on Long Face of Column (c) Least Preferable Arrangement of Dowels.

6.5 Detailing Requirements and Guidelines for Dowels

The interface between a column and a concrete foundation must be designed to adequately transfer vertical and hori-zontal forces between the members (ACI 13.2.2). ACI 16.3 contains design requirements for force transfer from a column to a footing.

Vertical compressive loads are transferred by bearing on the concrete or by a combination of bearing and reinforcement at the interface. Tensile loads must be resisted entirely by rein-forcement, which may consist of extended longitudinal bars, dowels, anchor bolts, or mechanical connectors. Lateral loads are transferred using the shear friction provisions of ACI 22.9 or other appropriate methods.

The amount of reinforcement that is required between a reinforced concrete column and footing depends on the type of stress in the bars of the supported member under all appli-cable load combinations. Minimum embedment lengths into both members also depend on this stress.

Dowels are commonly used as interface reinforcement between columns and footings. The dowel bars are set in the footing prior to casting the footing concrete and are subse-quently spliced to the longitudinal bars in the column. Dowel bars should never be driven or pushed into position in wet concrete. Where columns are supported on footings, the minimum area of reinforcement across the interface is equal to 0.5% of the gross area of the column (ACI 16.3.4.1).

To facilitate placement, a dowel should have a 90-degree hook on its end that rests on the bottom mat of the footing bars, as illustrated in Fig. 6.9b (Reference 16). If the dowel bars are de-tailed as shown in Fig. 6.9a, additional bars and bar supports are required to position the dowel bars higher in the depth of the footing, which is not cost effective.

The location of the dowels protruding from a footing can have an impact on the installation of the preassembled reinforc-ing cages of the columns (Reference 17). Dowels should be positioned so as not to interfere with the longitudinal bars or the tie hooks from the column.

Consider the arrangements of the column longitudinal bars and the dowel bars depicted in Fig. 6.10a. Except for the bars located adjacent to the center crosstie, the dowel bars are offset by 45 degrees from the column longitudinal bars rela-tive to the long side of the column. It is evident that there is no interference between the dowel bars and the 135-degree tie hooks in this arrangement. At the center crosstie, the dowel bars are located 90 degrees inboard relative to the long side of the column so that no interference occurs between them and the hooks of the crosstie. Depicted in Fig. 6.10b is the same column, but in this case, all of the dowel bars occur adjacent to the tie on the long side of the column. This arrangement is not as preferable as that shown in Fig. 6.10a, however, it is manageable because the ends of the hooks are relatively flexible and can be maneuvered around the dowels. Finally, Fig. 6.10c shows some of the dowel bars located on the long face of the column and some on the short face. This is the least preferable arrangement because there is more po-tential for difficulties during installation; lowering the column cage over the dowels will be challenging because the ties will not allow the same degree of flexibility as will the hooks at the ends of ties.




Fig. 6.11 Transverse Reinforcement Requirements for Columns in Intermediate Moment Frames.Fig. 6.12 Dimensional Limits of Columns in Special Moment Frames.

6.6 Detailing Requirements and Guidelines for SDC C

6.6.1 Overview

Requirements for columns that are part of an intermediate moment frame, which is the required SFRS for structures assigned to SDC C, are given in ACI 18.4.3. All of the requirements and guidelines presented above are also applicable.

6.6.2 Longitudinal Reinforcement Requirements

Limits for longitudinal reinforcement are given in ACI 10.6.1.1; these are the same limits for columns in buildings assigned to SDC A or B (see Section 6.2 of this Guide).

No restrictions are given on the location of splices of longitudi-nal reinforcement in columns in intermediate moment frames. However, as discussed in Section 6.6.3 of this Guide, the plastic hinge regions are anticipated to form at the ends of the column. Thus, it is good practice to locate lap splices outside of these regions.

6.6.3 Transverse Reinforcement Requirements

Transverse reinforcement requirements for columns in inter-mediate moment frame are given in ACI 18.4.3. Like beams, plastic hinges are anticipated to form at the ends of the col-umn where moments are usually maximum. As such, hoops or spirals are required at each end over the distance o. This length is indicated in Fig. 6.11, which is adapted from Refer-ence 7, for the case of transverse reinforcement consisting of hoops. The hoops provide confinement to ensure column duc-tility in the event of hinge formation during a seismic event.

Outside of the anticipated hinge length o, the spacing of the transverse reinforcement must conform to the lateral reinforcement provisions of ACI 25.7.2 for ties and ACI 25.7.3 for spirals, and to the provisions for spacing limits for shear reinforcement of ACI 10.7.6.5.2. The smallest spacing obtained from these requirements is to be used in the center region of a column outside of the plastic hinge zones.

The transverse reinforcement requirements of ACI 18.4.3.6 must be satisfied for columns that support reactions from discontinuous stiff members, such as walls.




Fig. 6.13 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu 0.3Ag f 'c and f '

c 10,000 psi.


6.7.1 Overview

Requirements for columns that are part of a special moment frame, which is the required SFRS for structures assigned to SDC D, E, or F, are given in ACI 18.7. All of the requirements and guidelines presented above are also applicable.

6.7.2 Dimensional Limits

Dimensional limits for columns in special moment frames are given in ACI 18.7.2.1. These limits have been guided by previous practice. A summary of these limits is given in Fig. 6.12, which is adapted from Reference 7. It is important that these limits are satisfied once the column dimensions have been initially estab-lished using the information in Section 6.2 of this Guide.

6.7.3 Longitudinal Reinforcement Requirements

Limits for longitudinal reinforcement are given in ACI 18.7.4.1. The lower limit is 0.01Ag and the upper limit is 0.06Ag, which is less than the upper limit for columns in buildings located

in all of the other SDCs. The main reason for this is to control steel congestion and the development of high shear stresses.

Lap splices of the longitudinal reinforcement must occur within the center half of the member length and must be enclosed with transverse reinforcement that conforms to ACI 18.7.5.2 and 18.7.5.3. The main reason for the location of the lap splices is to keep them away from the regions where plastic hinges are likely to form during a seismic event.

6.7.4 Transverse Reinforcement Requirements

Closely spaced transverse reinforcement, in the form of hoops or spirals, is required over the length o at each end of a column to confine the concrete because the largest bending moments are expected to occur at these locations, which could lead to flexural yielding.

Transverse reinforcement requirements are illustrated in Fig. 6.13, which is adapted from Reference 7, for columns reinforced with rectilinear hoops where Pu 0.3Ag f '

c and f 'c 10,000 psi.

Figure 6.14 depicts the details where Pu > 0.3Ag f 'c and/or

f 'c 10,000 psi.




Fig. 6.14 Transverse Reinforcement Requirements for Rectilinear Hoops in Columns of Special Moment Frames where Pu 0.3Ag f 'c and/or f '

c 10,000 psi.

Fig. 6.15 Transverse Reinforcement Requirements for Spiral or Circular Hoops in Columns of Special Moment Frames.




Fig. 6.16 Requirements of ACI 18.14.3.2(b) and (c) for Columns.

As mentioned previously, the use of crossties instead of closed ties are preferred mostly for ease of construction.

Requirements for columns reinforced with spiral and circular hoops are illustrated in Fig. 6.15, which is adapted from Refer-ence 7. Spiral reinforcement is generally the most efficient form of confinement reinforcement; however, the extension of the spirals into the beam-column joint usually causes construction difficulties, especially when placing longitudinal reinforcement from the beam through the joint.

6.8 Columns Not Designated as Part of the SFRS

Detailing requirements for columns that have not been as-signed to the SFRS are given in ACI 18.14.3.

In cases where the bending moments and shear forces in a column due to the lateral displacements from a seismic event do not exceed the design moment and shear strength of the beam, the detailing are illustrated in Fig. 6.16, which is adapted from Reference 7 where Pu 0.3Ag f '

c and f 'c 10,000 psi.

Where the induced bending and shear exceed the design mo-ment and shear strength of the beam, or where the induced moments and shear are not calculated, the detailing require-ments of ACI 18.14.3.3(c) are essentially the same as those for columns in special moment frames (see Section 6.7 of this Guide).




CHAPTER 7 Walls

7.1 OverviewGuidelines and recommendations on the economical design and detailing of walls are contained in this chapter. The focus is on walls found specifically in building structures; retaining walls, for example, are not covered. Information is provided on determining the wall thickness and detailing the longitudi-nal and transverse reinforcement. Specific requirements for special structural walls in structures assigned to SDC D, E, or F are given in Section 7.5 of this Guide.

7.2 Determination of Wall ThicknessIn typical building structures, reinforced concrete walls are usually located around stair and elevator openings. As such, the lengths of the walls are often dictated by the architectural requirements associated with these openings. In general, the thickness of a wall is determined based on strength require-ments for axial load, flexure, and shear and sometimes on ser-viceability requirements (overall building deflection), especially for high-rise buildings.

The thickness of a wall in a low-rise building can be governed by in-plane shear due to lateral forces, although a combination of axial load and out-of-plane bending due to lateral forces and/or eccentric gravity loads may control if the wall is rela-tively tall and slender. Where in-plane shear forces govern, the following equation can be used to determine a conservative estimate for the wall thickness h:

h = 0.8Vu

fc'

w

In this equation, which is based on ACI Eq. (11.5.4.4), Vu is the maximum factored shear force determined from the load com-binations in ACI Table 5.3.1 and w is the length of the wall. This equation will give a conservative value for h for walls of normal-weight concrete because the contribution of the transverse rein-forcement to the overall shear strength has not been included.

For relatively short walls subjected to only vertical loads, the simplified method of ACI 11.5.3 can be used to determine a preliminary wall thickness. The limitations of this method are the following: (1) the wall has a solid, rectangular cross-section and (2) the resultant of all applicable factored loads falls within the middle third of the wall thickness. Where these limitations are satisfied, ACI Eq. (11.5.3.1) is permitted to be used:

Pn = 0.55 fc' Ag 1 k c

32h

2

In this equation, c is the height of the wall and k is defined as follows:

• k 0.8 when the wall is restrained against rotation at one or both ends

• k 1.0 when the wall is unrestrained against rotation at both ends

This equation can be solved for h (where Ag h w ) for a given set of design criteria:

h = Pn1.1 fc

'w+ Pn

1.1 fc' lw

2

+k c32

2

Relatively tall and/or slender walls are generally governed by a combination of axial load and in-plane bending moments. The strength design method must be used to design the wall in such cases. A wall thickness and the size and spacing of the longitu-dinal reinforcement are assumed so that an interaction diagram can be constructed. Applicable load combinations for combined axial load and bending can then be checked. Because there is no closed-form solution for multiple load cases, iterations must be performed until all strength design criteria are satisfied.

In addition to satisfying all strength and serviceability requirements, wall thicknesses are sometimes provided that make the columns in the building part of a nonsway frame (that is, the frame is braced against sidesway). This can be advantageous especially in situa-tions where the columns are slender; secondary effects increase dramatically with increasing sway. ACI 6.2.5 permits columns to be considered braced against sidesway when the bracing elements in the structure (typically, walls or a combination of walls and moment frames) have a total lateral stiffness in the direction of analysis of at least 12 times the gross lateral stiffness of all the columns within a given story. This criterion can be used to determine the thicknesses of the walls to produce a nonsway frame.

7.3 Minimum ReinforcementMinimum longitudinal and transverse reinforcement depend on the magnitude of the in-plane factored shear force Vu. The minimum longitudinal (vertical) distributed reinforcement ratio and the minimum transverse (horizontal) distributed reinforcement ratio t are given in Table 7.1 where Vu 0.5 Vc for deformed bars in cast-in-place concrete. Table 7.1 is based on Table 11.6.1 of ACI 318.

Table 7.1 Minimum Reinforcement Ratios where Vu 0.5 Vc

Bar Size f y(psi) Minimum Minimum t

≤#560,000 0.0012 0.0020

60,000 0.0015 0.0025

>#5 Any 0.0015 0.0025

The limits in this table need not be satisfied if it can be dem-onstrated by structural analysis that the wall has adequate strength and stability.

Where Vu 0.5 Vc, the following requirements must be satisfied:

• greater of 0.0025+ 0.5 2.5 hw / w( ) t 0.0025( )0.0025

• t 0.0025

Note that need not exceed t.




Fig. 7.1 Rustication Over Entire Length or Height of a Wall.

Fig. 7.2 Rustication Over a Portion of a Wall (a) Minimum Concrete Cover Not Provided (b) Offset Bars (c) Inner Layer of Bars.

(a)

(b)

(c)

7.4 Detailing Requirements and Guidelines for Reinforcement

7.4.1 Overview

As noted in the previous section, the size and spacing of the longitudinal and transverse reinforcement in a wall must be chosen to satisfy all applicable requirements for strength and serviceability. This section provides a summary of the require-ments in ACI 318 and includes guidelines that can be used to obtain more economical walls.


Concrete protection for reinforcement plays an important role in the formulation of the requirements of bar spacing and bar development. Reinforcing bars are placed in a concrete mem-ber with a minimum concrete cover to protect it from weath-er, fire, and other effects. Minimum cover requirements for nonprestressed, cast-in-place concrete construction are given in ACI Table 20.6.1.3.1. For walls, concrete cover is measured from the surface of the concrete to the outer edge of the layer of reinforcement closest to the wall surface.

Where reveals or rustications run the entire length or height of a wall, the minimum required cover to the reinforcing bars is indicated in Fig. 7.1 (Reference 6). A constant concrete cover is maintained from the inside of the reveal to the surface of the wall.

Potential problems with the minimum required concrete cover can occur where rustications are located at specific areas of a wall (see Fig. 7.2a). It is clear from the figure that the cover to the transverse reinforcement is smaller than that which is required. One solution is to offset the reinforcing bars in the localized area to maintain the required cover (see Fig. 7.2b). The detailing and placing of the reinforcement can become quite challenging if more than one area of rustication is re-quired and/or if the rustication is located near an opening in a wall. A more viable solution is to treat the rustication area as an opening and provide an inner layer of reinforcement with the proper cover (see Fig. 7.2c). This reinforcement should be developed beyond the rustication area in all directions.

7.4.3 Spacing Requirements

Spacing requirements for longitudinal and transverse rein-forcement walls are given in ACI 11.7.2 and 11.7.3, respectively. The spacing of longitudinal bars in cast-in-place walls should not exceed the lesser of 3 times the wall thickness and 18 in. For shear reinforcement that is required for in-plane shear, the spacing is limited to one-third of the length of the wall.

The maximum spacing is also the lesser of 3 times the wall thickness and 18 in. for spacing of the transverse bars. The spacing is limited to one-fifth of the length of the wall for shear reinforcement that is required for in-plane shear.

Walls that are greater than 10 in. in thickness are required to have two layers of reinforcement in both directions and distributed in accordance with the provisions in ACI 11.7.2.3. Flexural tension reinforcement is to be well distributed and placed as close as practical to the tension face of the wall.

Like for beams and slabs, the longitudinal and transverse bars in reinforced concrete walls must be spaced at a sufficient distance so that concrete can flow easily between the bars and between the bars and the formwork. According to ACI 25.2.3, the minimum clear distance that is to be provided between bars is equal to the largest of the following:

• 1.5 times the diameter of the longitudinal bar

• 1.5 in.

• ( 4/3) times the diameter of the largest aggregate in the concrete mix

To simplify placement of the reinforcement in the field, bars should be placed at a consistent spacing or using multiples of a given spacing. Similarly, to avoid installation errors, the same bar size should be used in both the longitudinal and transverse directions.

7.4.4 Lateral Support of Longitudinal Reinforcement

In cases where the longitudinal reinforcement in a wall is required for axial strength or where the area of the longitudinal reinforce-ment exceeds 1% of the gross area of the wall, transverse ties are required around the longitudinal reinforcement (ACI 11.7.4).




#

#

Fig. 7.3 Typical Reinforcement at Wall Openings.

Fig. 7.4 Preferred Reference Point for Development Length of Trim Bars.

Fig. 7.5 Development Length of Trim Bars Measured from Perpendicular Trim Bars.

While it may be feasible to provide such ties in thicker walls, it is very difficult to do so in thinner walls, especially where the bars are spaced relatively close together. Development of the tie bars and interference of the adjoining hooks at the ends of the ties can pose major problems.

7.4.5 Wall Openings

In a typical building, it is inevitable that openings of various sizes and shapes for doors, windows, conduit, piping, and ductwork will need to be made in the structural walls. Me-chanical, plumbing, and electrical openings are usually located just below the slab, but, in general, could occur anywhere.

Additional reinforcement must be provided around the perimeter of wall openings and it is commonly referred to as trim bars, opening bars, or corners bars (Reference 18). In essence, these bars are to replace the reinforcement interrupted by the opening.

ACI 11.7.5 requires that for walls with one layer of reinforce-ment in both the longitudinal and transverse directions, at least one #5 bar must be provided around an opening. Similarly, at least two #5 bars are required around openings in walls that have two layers of reinforcement in both directions. These are the minimum amounts of reinforcement that is required; in walls subjected to relatively large lateral loads, for example, an analysis of the wall must be made and the required amounts of reinforcement in the wall and around the perimeter of the openings must be provided based on the analysis. Regardless of the size and amount of the required reinforcement, the trim bars must be fully anchored to develop the yield strength of the bars in tension at the corners of an opening.

Unless required for structural purposes, longitudinal trim bars around the sides of an opening that run the full height of a wall and that get lap spliced with dowels protruding from the footing

should be avoided (see Fig. 7.3). Detailing and placing full-height trim bars can be a problem because the exact locations of the wall openings may not be available at the time the concrete for the footing is placed; thus, the dowels may not be at the correct location. As noted above, longitudinal trim bars need to be developed only past the edge of the opening. Providing full-height bars when they are not required is not recommended.

In regards to the development length of the trim bars, the preferred reference point to measure the development length from is the corner of the opening, as shown in Fig. 7.4. This is an advantageous location for the detailer and placer because it is a fixed point. Measuring the embedment length from a longi-tudinal or transverse trim bar is frequently done, but the embed-ment length may wind up being too short if the perpendicular trim bars adjacent to the open-ing shift for whatever reason from their intended location (see Fig. 7.5).




Fig. 7.6 Reinforcement Details for Column-like Wall Segments.

Fig. 7.7 Cut Wall Bars Replaced One-for-one with Trim Bars.

Fig. 7.8 Cut Wall Bars Replaced with Larger Trim Bars.

Fig. 7.9 Diagonal Bar Development.

It is very important to indicate on the structural drawings the limitations for typical reinforcement around an opening. When openings become relatively wide or long, portions of the wall may behave more like beams or columns and they need to be detailed accordingly. For example, for relatively wide open-ings, the segment of the wall above and below the opening may require beam-type reinforcement (longitudinal bars and stirrups). Similarly, vertical wall segments adjacent to an open-ing may behave more like columns and should be detailed as such. Recommended details are illustrated in Fig. 7.6.

The spacing of the trim bars need to be indicated on the struc-tural drawings as well.

In cases where a large number of bars are cut either because of the size of the opening or the amount of reinforcement that is required in the wall, a large amount of trim bars will be required on each side of the opening. Some of the bars may be too far from the opening to be considered fully effective if the same bar size is used for the trim bars as in the wall. This is illustrated in Fig. 7.7 where the cut wall bars are replaced one-for-one with trim bars.

A possible solution to this is to use fewer bars that are larger. This is illustrated in Fig. 7.8 for the case depicted in Fig. 7.7.

The main purpose of the diagonal bars at the corners of openings is to arrest cracks that can form at these reentrant corners. For openings that occur close to the top of a wall or where openings are stacked on top of each other, the typical straight diagonal bar detail may not be possible. In order to properly develop the diagonal bars, either a standard hook needs to be provided at one end or the bar can be bent, as illustrated in Fig. 7.9 for the case of stacked openings.

7.4.6 Wall Corners and Intersections

The reinforcement at wall corners and intersections need to be carefully detailed to avoid installation and other problems. Long transverse bars with hooks at one or both ends should be avoided because they are very difficult to install. Wall bars are often assembled in curtains or mats that are lifted into position. Hooks complicate preassembly, transportation, stor-age, and handling of the curtains. Constructability is enhanced by providing straight horizontal bars that are lapped spliced together by separate bars; by doing so, adjacent curtains can be installed without interference (Reference 19). Furthermore, the curtains can easily be adjusted to maintain proper con-




Fig. 7.10 Wall Corner and Intersection Details that Should Be Avoided – Single Layers of Transverse Reinforcement.

Fig. 7.11 Preferred Wall Corner and Intersection Details – Single Layers of Transverse Reinforcement.

Fig. 7.12 Wall Corner Details That Should Be Avoided – Double Layers of Transverse Reinforcement.

Fig. 7.13 Preferred Wall Corner Details – Double Layers of Transverse Reinforcement.

Fig. 7.14 Wall Intersection Detail That Should Be Avoided – Double Layers of Transverse Reinforcement.

Fig. 7.15 Preferred Wall Intersection Details – Double Layers of Transverse Reinforcement.

0 in. (typ.)

Fig. 7.17 Standard Details at Wall Corners (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the Transverse Bars.

Fig. 7.16 Common Reinforcement Detail at Wall Corners (sp is the center-to-center distance between bars).

(a) (b)

(a) (b) (c)

(a) (b)

crete cover as the independent hooked bars used for the lap splices are tied in place. The costs associated with the extra reinforcing bars needed for the lap splices are far outweighed by the costs associated with the labor needed for increased handling and installation of the bars with hooks on the ends.

Depicted in Fig. 7.10 are three examples of details at corners and intersections that should be avoided in walls with one layer of trans-verse reinforcement because of the reasons noted above. Illus-trated in Fig. 7.11 are the preferred details, which show the separate hooked bars that are doweled to the straight bars in the wall.

The details shown in Fig. 7.12 at the corners of walls with two layers of transverse reinforcement with hooks on their ends should be avoided because they make it difficult to use preassembled curtains of bars. Of the three arrangements illustrated in Fig. 7.13, detail a is common, but detail b is pre-ferred because the separate 90-degree hooked bars that are lap spliced with the two preassembled double-bar curtains of transverse reinforcement is easy to construct. Detail c is also easy to construct for preassembled curtains but it can only be used in walls that are thick enough to accommodate the width of the U bars (hairpins) at the ends that are lap spliced to the transverse reinforcement in the walls.

The detail illustrated in Fig. 7.14 should be avoided at wall intersections for the reasons stated previously. The preferable layouts are shown in Fig. 7.15. Once again, the layout in Fig. 7.15b is only possible in relatively thick walls.

The location of the longitudinal bars at wall corners and inter-sections must also be carefully investigated (Reference 20). Depicted in Fig. 7.16 is a common detail for bar arrangement at a corner of a wall. The location of the longitudinal bars at the corner appears to be reasonable, but problems become readily apparent once transverse bars are included (see Fig. 7.17).




Fig. 7.18 Preferred Details at Wall Corners (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located outside of the Transverse Bars.

Fig. 7.19 Common Reinforcement Detail at Wall Intersections.

Fig. 7.20 Standard Details at Wall Intersections (a) Longitudinal Bars Lo-cated Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the transverse Bars.

(a) (b)

(a)

(b)

Fabrication and placing tolerances for the transverse bars in the wall can result in an irregular layout at the corner. Because of this, placing a longitudinal bar at the intersection of the transverse bars is not possible. Instead, the longitudinal bar will need to be offset from this working point.

As noted above, the transverse bars in the wall at the corner will be lap spliced together by a separate hooked bar. The fabrication tolerance for the bend radius of this bar and the angular deviation of the corner bars in the wall also make it dif-ficult to locate and tie the longitudinal bar on the outside face. Furthermore, if the two outside face curtains of reinforcing steel were preassembled, it would be difficult to locate the corner longitudinal bar once the curtains have been erected and the transverse corner bars have been placed.

The details illustrated in Fig. 7.18 are preferred because the single longitudinal bar shown in Fig. 7.17 has been replaced with two longitudinal bars (one on each wall located slightly away from the corner). These longitudinal bars can be easily placed, especially if the curtains are preassembled.

A similar situation occurs at wall intersections. Depicted in Fig. 7.19 is a common detail for bar arrangement at a wall intersection. Figure 7.20 shows the same detail with the trans-

verse bars. It is evident that the longitudinal bar that is located on the inside face of the core is not needed and only adds to congestion at this location.

Illustrated in Fig. 7.21 is the preferred detail for the longitudinal bars at a wall intersection.




Fig. 7.21 Preferred Details at Wall Intersections (a) Longitudinal Bars Located Outside of the Transverse Bars (b) Longitudinal Bars Located Inside of the Transverse Bars.

Fig. 7.22 Web Reinforcement Requirements for Grade 60 Bars in Special Structural Walls.

(a) (b)


7.5.1 Overview

Special structural walls are required in structures assigned to SDC D, E, or F that utilize bearing wall systems, building frame systems, and dual systems. Detailing requirements for such walls are given in ACI 18.10. All of the requirements and guidelines presented above are also applicable.

The requirements in ACI Chapter 11 are applicable to walls in structures assigned to SDC A, B, and C. Unlike two-way slabs without beams, beams, and columns, there are no separate

requirements for walls in structures assigned to SDC C; it is assumed that the provisions in ACI Chapter 11 provide the required level of ductility in such cases.

7.5.2 Web Reinforcement Requirements

The provisions of ACI 18.10.2.1 for required web reinforce-ment in special structural walls are summarized in Fig. 7.22, which is adapted from Reference 7. Reinforcement provided for shear strength must be continuous and uniformly distrib-uted across the shear plane. This uniform distribution helps control the width of inclined cracks.




Fig. 7.24 Reinforcement Details Where Special Boundary Elements are not Required and the Provisions of ACI 18.10.6.5 are Met.

Fig. 7.23 Design and Detailing Requirements for Special Boundary Elements.

7.5.3 Boundary Elements

During a seismic event, the ends of a wall and the edges adjacent to openings can be subjected to large compressive forces as the wall undergoes cyclic deformations. Special transverse reinforcement may be required at these loca-tions to confine the concrete and to restrain the longitudinal reinforcement in the wall so that buckling of the bars does not occur.

Two methods to determine whether special elements are required or not are given in ACI 18.10.6.2 and 18.10.6.3.

Regardless of the method, the detailing requirements of ACI 18.10.6.4 must be satisfied. A summary of these require-ments is given in Fig. 7.23, which is adapted from Reference 7.

Even though special boundary elements may not be required, additional transverse reinforcement at the ends of the wall may be required where the provisions of ACI 18.10.6.5 are met. The reinforcement details in this case are illustrated in Fig. 7.24, which is adapted from Reference 7.




Fig. 8.1 Location of Reinforcement Resisting Tension Due to Moment and Axial Force (ACI 12.5.2.3).

CHAPTER 8 Diaphragms

8.1 OverviewGuidelines and recommendations on the economical design and detailing of conventionally reinforced, cast-in-place diaphragms and collector elements are contained in this chapter. Informa-tion is provided on determining the thickness and detailing the longitudinal and transverse reinforcement. Specific requirements for diaphragms and collectors in structures assigned to SDC D, E, or F are given in Section 8.4 of this Guide.

8.2 Determining the Diaphragm ThicknessIn general, the thickness of a diaphragm must be sufficient to resist in-plane bending moments, shear forces, and axial forces due to the combinations of gravity and lateral loads.

ACI Chapter 12 requires that floor and roof diaphragms in buildings assigned to SDCs A through C have a thickness not less than that required for floor and roof elements that are contained in other chapters of ACI 318. Thus, diaphragms can be initially checked for the applicable load combinations using the thickness determined by the information provided in Chapters 3 and 4 of this Guide. There are no minimum thick-ness requirements prescribed in ACI Chapter 12.

8.3 Detailing Requirements and Guide-lines for Reinforcement

The reinforcement that is required in the diaphragm is deter-mined using the applicable load combinations for axial force, bending moment, and shear force.

According to ACI 12.5.2.3, nonprestressed chord reinforcement must be located within h/4 of the tension edge of the dia-phragm where h is the depth of the diaphragm in the direction of analysis (see Fig. 8.1, which is adapted from Reference 7). This helps ensure that the shear flow through the depth of the diaphragm is uniform.

Chord reinforcement is usually positioned near the edge of the diaphragm and is placed within the middle third of the slab or beam depth to minimize interference with the slab or beam longitudinal reinforcement. Furthermore, at this position, the chord reinforcement has a minimal effect on the flexural strength of the slab or beam.

Required transverse reinforcement for shear is commonly incorporated into the bottom mat of the uniformly distributed reinforcement in the slab. It is important to call out the required lap splice lengths for these bars on the structural drawings because they may exceed the lengths that are required for the typical slab reinforcement.

Collector reinforcement is typically located within the mid-depth of the slab, similar to chord reinforcement. The amount of collector reinforcement is determined based on the applicable load combinations for combined axial force and bending moment. In cases where the slab is not suf-ficient to act as a collector, beams must be provided. The requirements and guidelines given in Chapter 5 can be used in such cases.




Fig. 8.2 Detailing Requirements for Diaphragms and Collectors in Buildings Assigned to SDC D, E, or F.


8.4.1 Overview

Earthquake design forces for diaphragms are to be obtained from the general building code using the applicable provisions and load combinations. In the case of the IBC and ASCE 7, the load combinations amplify the code-prescribed earthquake forces by the overstrength factor o for collectors and their connections in structures assigned to SDCs C through F. The overstrength factor represents an upper bound lateral strength and is appropriate to use when estimating the maximum force that can be developed in nonyielding elements of the SFRS during an earthquake. The intent of this requirement is to ensure that collectors and their connections have adequate strength and remain essentially elastic during a design event.

8.4.2 Minimum Thickness

A minimum thickness of 2 in. is prescribed in ACI 18.12.6 for concrete slabs. This reflects the current practice in joist and waffle slab systems in cast-in-place concrete. As always, it is important to consider the fire-resistance requirements when selecting an overall slab thickness.

8.4.3 Minimum Reinforcement

The minimum reinforcement ratios for the longitudinal and transverse reinforcement in a diaphragm must conform to those for temperature and shrinkage given in ACI 24.4. The maximum spacing of 18 in. is intended to control the width of inclined cracks that may form during a seismic event.

Bar development and lap splices in diaphragms and collec-tors are to be determined in accordance with ACI 25.4.2 and 25.5.2. Reductions in development or splice lengths are not permitted in structures assigned to SDCs D, E, or F.

The requirements for chord reinforcement are the same as those discussed in Section 8.3 of this Guide (see Fig. 8.1).

Collectors must be designed for the combined effects due to flexure, shear, and axial compression or tension caused by the gravity and seismic load effects. Transverse reinforcement conforming to ACI 18.7.5.2(a) through (e) and ACI 18.7.5.3 must be provided in collectors where the compressive stress in the collector is greater than 0.2f '

c (ACI 18.12.7.5). An exception is that the spacing limit of ACI 18.7.5.3(a) should be one-third the least dimension of the collector. Confining reinforcement may be discontinued where the compressive stress is less than 0.15f '

c. In cases where the forces have been amplified by o, the limits above are increased to 0.5f '

c and 0.4f '

c, respectively.

Detailing requirements for the longitudinal reinforcement in collectors at splice and anchorage zone locations are given in ACI 18.12.7.6. A summary of these requirements and the other noted previously are illustrated in Fig. 8.2, which is adapted from Reference 7.

Like all elements that are part of the SFRS, it is good prac-tice to ensure that the reinforcement in the diaphragms and collectors can adequately fit within the sections and that the connection and intersecting locations are not too congested.




CHAPTER 9 Foundations

9.1 OverviewGuidelines and recommendations on the economical design and detailing of spread footings, mat foundations, drilled piers, and grade beams are contained in this chapter. Information is provided on sizing the members and detailing the reinforce-ment. Specific requirements for foundations in structures as-signed to SDC D, E, or F are given in Section 9.6 of this Guide.

9.2 Spread Footings

9.2.1 Material Selection

Normal-weight concrete with a compressive strength of 3,000 psi is usually the most economical choice for footings. Higher strength concrete may be used for various reasons, but usu-ally the savings in concrete volume does not offset the higher cost.

Grade 60 reinforcing bars are recommended for overall economy.

9.2.2 Determining the Base Dimensions and Thickness

The base area of a symmetrically loaded, individual footing is determined by dividing the unfactored loads acting on the sup-ported member by the net permissible soil pressure, which is the allowable bearing capacity of the soil minus the weight of the surcharge above the footing. The allowable soil bearing ca-pacity is typically obtained from a geotechnical report or from local building authorities. Individual spread footings are usually made square and are centered under the column it supports. Rectangular footings may be required where there are space limitations, such as adjacent to property lines.

For footings subjected to an axial load and bending moment or, equivalently, to an axial load acting at an eccentricity, the pressure beneath the footing is not uniform. Base dimensions need to be provided such that the maximum pressure is less than or equal to the net permissible soil pressure.

Once the required area of the footing Af has been estab-lished, the thickness of the footing must be determined considering both flexure and shear. The location of the critical section for flexure is given in ACI Table 13.2.7.1. For a con-centrically loaded, square footing with a minimum amount of Grade 60 reinforcement (reinforcement ratio of 0.0018) and 3,000 psi, normal-weight concrete supporting a square column, the following equation can be used to determine the effective depth d of the footing:

d = 2.2c PuAf

In this equation, c is the distance from the face of the column to the edge of the footing (in feet), Pu is the factored axial force on the column (in kips), and Af is the base area of the footing (in square feet). The resulting effective depth d is in inches.

The depth of the footing that is provided must also satisfy one-way and two-way shear requirements. The critical section for one-way shear in a footing is located a distance d from the face of the column. The minimum effective depth d that satis-fies one-way shear requirements can be obtained from the following equation for normal-weight, 3,000 psi concrete:

d =quc

qu + 82

In this equation, qu is the factored pressure at the base of the square footing (in psi). The distance c is in inches as is the effective depth d.

The critical section for two-way shear is located a distance of d/2 from the face of the column. The minimum effective depth d that satisfies two-way shear requirements can be obtained from the following equation for normal-weight, 3,000 psi concrete:

d = c1

qu2+164 +

qu2+164

2+ qu

qu4+164

Af

c12 1

2 qu4+164

In this equation, c1 is the dimension of the square column (in inches), qu is the factored pressure at the base of the square footing (in psi), and Af is the area of the square footing (in square inches). The effective depth d is in inches. Two-way shear is usu-ally more critical than one-way shear. Because shear reinforce-ment is not economical in footings, the depth of the footing must be increased where shear capacity is not sufficient.

The largest d computed by these three equations is to be used in determining the overall thickness of the footing. Because the minimum cover to the reinforcement is equal to 3 in. for concrete cast against and permanently exposed to earth (ACI Table 20.6.1.3.1), the overall depth of the footing should be taken equal to at least 4 in. plus the effective depth d. Note that the minimum d required by ACI 13.3.1.2 is 6 in.


Reinforcement

Flexural Reinforcement

Requirements for the distribution of flexural reinforcement in two-way footings are given in ACI 13.3.2.2 and 13.3.3.3. For square footings, the reinforcement is to be distributed uniformly across the entire width of the footing in both direc-tions. In the case of rectangular footings, the reinforcement must be distributed in accordance with the requirements in ACI 13.3.3.3, which are illustrated in Fig. 9.1. Reinforcement in the long direction is uniformly distributed across the entire width. A portion of the reinforcement in the short direction is banded over the column with the remainder uniformly distrib-uted outside of the band width.




Fig. 9.1 Distribution of Flexural Reinforcement in a Rectangular Footing.

In order to minimize the potential for errors while placing the bars in the short direction, a common practice is to increase the amount of reinforcement in the short direction by 2 /( 1) (where is the ratio of the long side to the short side of the footing) and space it uniformly across the long dimension of the footing instead of distributing the bars as shown in Fig. 9.1.

Flexural reinforcement in footings must be fully developed in accordance with the applicable provisions of ACI Chapter 25. For a concrete column supported by an isolated footing, the required development length d must be less than or equal to the available development length:

dL c1

2 3 in.

In this equation, L and c1 are the lengths of the footing and column in the direction of analysis, respectively.

In typical cases, the clear spacing and cover requirements in the first row of ACI Table 25.4.2.2 are satisfied for flexural reinforce-ment in footings. Table 9.1 contains the minimum development lengths d based on those requirements for normal-weight, 3,000

psi concrete and Grade 60 reinforcement that is uncoated and is placed at the bottom of the footing (i.e., not top bars).

Reinforcement Across the Interface

The amount of reinforcement that is required at the interface be-tween the column and the footing depends on the type of stress in the bars of the column under all applicable load combinations.

Dowels are commonly used as interface reinforcement be-tween columns and footings. The dowels are set in the footing prior to casting the footing concrete and are subsequently spliced to the column bars.

In cases where the column bars are all in compression and the factored bearing load Bu is less than or equal to the design bearing strength Bn , which is determined in accordance with ACI Table 22.8.3.2, a minimum area of reinforcement across the interface is required; this minimum amount is 0.5% the area of the column. Where Bu > Bn , the required area of interface reinforcement As can be obtained from the following equation:

As =Bu Bn

f y0.005Ag

Illustrated in Fig. 9.2 are dowels across the interface between a column and footing. For the case where all of the column bars are in compression, the dowels must extend into the footing a compression development length dc determined in accor-dance with ACI 25.4.9.2. The dowel bars are usually hooked and extend to the level of the flexural reinforcement in the footing. According to ACI 25.4.1.2, the hooked portion of the dowels cannot be considered effective for developing the dowel bars in compression. The following equation must be satisfied to ensure adequate development of the dowels in the footing:

h dc r (db)dowel 2(db)f cover

In this equation, r is the radius of the dowel bar bend, and (db)dowel and (db)f are the bar diameters for the dowel bars and the flexural reinforcement, respectively.

Dowels must also be fully developed into the column; they are typically lap spliced to the column bars.

Tensile forces (either direct or transferred by a moment) must be resisted entirely by reinforcement across the interface. Ten-sile anchorage of the dowel bars into the footing is typically accomplished by providing a 90-degree standard hook at the ends of the dowel bars. A tension lap splice must be provided between the dowel bars and the column reinforcement.

ACI 16.3.3.5 permits the shear-friction method of ACI 22.9 to be used for transfer of lateral loads from a supported member to a footing.

Additional design and detailing requirements for dowels can be found in Section 6.5 of this Guide.

Reference 21 contains additional information on the design of individual footings, including design tables that give material quantities of concrete and reinforcement for a wide variety of cases.

Table 9.1 MinimumTension Development Length for

Flexural Reinforcement in Footings

Bar Size Development length, d (in.)

#4 22

#5 28

#6 33

#7 48

#8 55

#9 62

#10 70

#11 78




Fig. 9.2 Footing Dowels.

Fig. 9.3 Typical Reinforcement Configuration in a Deep Mat Foundation.

9.3 Mat Foundations

9.3.1 Overview

Mat foundations are used to support all or a portion of the vertical elements in a building. They are commonly specified where erratic or relatively weak soil strata are encountered or where a large number of closely spaced spread footings would be required.

The plan dimensions of a mat foundation are typically dictated by the geometry of the building it supports, including the layout of the vertical elements (columns and walls). Property lines and other factors may also influence plan dimensions. It is impor-tant to provide dimensions so that the soil pressure beneath the mat does not exceed the net permissible soil pressure.

The reinforcing system in a mat foundation can be substantial depending on a number of factors. Improper detailing of the reinforcement can result in constructability issues that can impact schedule and cost (Reference 22). The following infor-mation describes ways to simplify the design, detailing, and placement of the required reinforcement in a mat foundation.

9.3.2 Determining the Mat Thickness

The thickness of a mat foundation is typically controlled by shear requirements. Both one-way and two-way shear must be investigat-ed around the critical sections of the vertical members supported by the mat. Like footings, it is common practice not to use shear reinforcement in mats. The thickness of the mat is usually increased where additional shear capacity is needed. For overall economy, the thickness of the mat is constant over its entire extent.


Reinforcement

Once the thickness of the mat has been established and the required amounts of reinforcement are calculated at the criti-cal sections, a suitable bar size and spacing must be selected. The provided area of reinforcement must be greater than or equal to the minimum reinforcement prescribed in ACI 8.6.1.1 for two-way slabs (ACI 13.3.4.4).

For deep mats, the reinforcing bars can be placed in two layers (one mat) at both the top and bottom faces or in four layers (two mats). Bars that are in the interior layers should be aligned with those in the outer layer (see Fig. 9.3). This helps reduce voids in the concrete because it provides clear pas-sage for concrete placement.




Fig. 9.4 Dowels in a Mat Foundation.

Fig. 9.5 Elevator Pit in a Mat Foundation.

Fig. 9.6 Trench Drain in a Mat Foundation (a) Design Detail; and (b) Reinforcing Bar Placing Detail.

(a)

(b)

The size of the bars in the interior layers should be the same size as or smaller than the bars in the outer layers. It is recommended that a 3-in. spacing be provided between the bars to facilitate concrete placement.

In cases where additional bars are required in localized areas that are heavily loaded, these bars should be spaced as a multiple or sub-multiple of the spacing for the typical flexural reinforcement.

Where the column spacing is not on a regular, symmetric grid, the layout of the reinforcing bars in the mat should be placed on an orthogonal grid and should not be skewed to follow the column layout. Additional bars can be placed at locations in the regular grid wherever required. This greatly simplifies placing the bars in the field.

Staggering the splices for different layers of reinforcing bars leads to confusion in the field with respect to placing and inspecting the bars. Avoiding staggered splices is the preferred method of placement for ease of constructability. Using the maximum straight bar length as often as possible usually minimizes the number of lap splices.

Like columns supported by spread footings, the dowels from the columns and walls that are supported by the mat should extend to the bottom layer of flexural reinforcement in the mat (see Fig. 9.4). The dowels should have a 90-degree standard hook at the bottom end; this allows the dowels to be tied to both the top and bottom layers of reinforcement in the mat, which secures the dowels from displacing before or during concrete placement.

Mat foundations will usually have to incorporate pits for eleva-tors or sumps. Where the depth of the mat can accommodate the pit, additional layers of reinforcing steel can be added to serve as the top steel in the mat (see Fig. 9.5). An analysis should be performed to determine if the interrupted top bars

in the mat require hooks at the ends or not. If the depth of the mat cannot accommodate the pit, it can be locally thickened as shown in Fig. 9.6 for the case of a trench drain.

9.4 Drilled Piers

9.4.1 Overview

A drilled pier, which is sometimes referred to as a pier or caisson, transfers the loads from the superstructure to a soil or rock stratum that is usually well below the ground surface. The bottom of the shaft is often belled out to provide a larger end-bearing area. Concrete is deposited into the shaft after the reinforcement has been set in place.

The loads from the supported member are transferred to the shaft by bearing. Skin friction, point bearing, and a combination of the two are ways in which the load is transferred to the soil surrounding and below the shaft or bell.




Cover

Fig. 9.7 Reinforcement Details for Drilled Piers Subjected to Axial Compression loads.

9.4.2 Determining the Shaft Diameter

Table 1810.3.2.6 in the 2015 IBC (Reference 25) contains allowable stresses for deep foundation elements, including drilled piers. The allowable stress in compression for cast-in-place concrete with a permanent casing is 0.4f '

c and is 0.3f 'c

where permanent casing is not provided.

The diameter of the shaft can be determined from the following equation where permanent casing is not provided:

dshaft =4P0.3 fc

'( )

1/2

In this equation, P is the total service axial dead and live load acting on the drilled pier. The diameter is typically specified in multiples of 6 in.

Table 9.2 contains the maximum allowable axial load that can supported by a drilled pier shaft for allowable stresses of 0.25f '

c and is 0.30f '

c.

9.4.3 Determining the Bell Diameter

For end-bearing drilled piers, the diameter of the bell can be determined from the following equation:

dbell =4Pqa

1/2

In this equation, qa is the allowable bearing capacity of the soil or rock.

Table 9.3 contains the safe bearing load for bells as a function of bell diameter and allowable soil/rock bearing pressure.


Reinforcement

Recommended reinforcement details for drilled piers are given in Fig. 9.7. A minimum longitudinal reinforcement ratio of 0.005 is used, which corresponds to the ratio that is permit-ted in ACI 10.3.1.2 for columns with cross-sections that are larger than required for the applied loads.

Table 9.2 Shaft Maximum Allowable Axial Loads (kips)

Shaft

Diameter

(ft-in.)

Shaft

Area

in.2

Shaft Maximum Allowable Axial Load—Kips*

fc 0.25f 'c fc 0.30f '

cf '

c 3,000 psi

f 'c

4,000 psif '

c 5,000 psi

f 'c

6,000 psif '

c 3,000 psi

f 'c

4,000 psif '

c 5,000 psi

f 'c

6,000 psi1-6 254 191 254 318 382 229 305 382 458

2-0 452 339 452 565 679 407 543 679 814

2-6 707 530 707 884 1060 636 848 1060 1272

3-0 1018 763 1018 1272 1527 916 1221 1527 1832

3-6 1385 1039 1385 1732 2078 1247 1663 2078 2494

4-0 1810 1357 1810 2262 2714 1629 2171 2714 3257

4-6 2290 1718 2290 2863 3435 2061 2748 3435 4122

5-0 2827 2121 2827 3534 4241 2545 3393 4241 5089

5-6 3421 2566 3421 4276 5132 3079 4105 5132 6158

6-0 4072 3054 4072 5089 6107 3664 4886 6107 7329

6-6 4778 3584 4778 5973 7168 4301 5734 7168 8601

7-0 5542 4156 5542 6927 8313 4988 6650 8313 9975

*For shafts designed as plain concrete piers, laterally braced by soil.




Table 9.3 Bell Safe Bearing Load (kips)

Bell

Diameter

(ft-in.)

Bearing

Area

(ft2)

Bell Safe Bearing Load Kips**

10,000 psf ** 12,000 psf ** 15,000 psf ** 20,000 psf ** 25,000 psf ** 30,000 psf **

1-6 1.77 18 21 27 35 44 53

2-0 3.14 31 38 47 63 79 94

2-6 4.91 49 59 74 98 123 147

3-0 7.07 71 85 106 141 177 212

3-6 9.62 96 115 144 192 241 289

4-0 12.57 126 151 188 251 314 377

4-6 15.90 159 191 239 318 398 477

5-0 19.63 196 236 295 393 491 589

5-6 23.76 238 285 356 475 594 713

6-0 28.27 283 339 424 565 707 848

6-6 33.18 332 398 498 664 830 995

7-0 38.48 385 462 557 770 962 1155

7-6 44.18 442 530 663 884 1104 1325

8-0 50.27 503 603 754 1005 1257 1508

8-6 56.75 567 681 851 1135 1419 1702

9-0 63.62 636 763 954 1272 1590 1909

9-6 70.88 709 851 1063 1418 1772 2126

10-0 78.54 785 942 1178 1571 1963 2356

10-6 86.59 866 1039 1299 1732 2165 2598

11-0 95.03 950 1140 1425 1901 2376 2851

11-6 103.87 1039 1246 1558 2077 2597 3116

12-0 113.10 1131 1357 1696 2262 2827 3393

12-6 122.72 1227 1473 1841 2454 3068 3682

13-0 132.73 1327 1593 1991 2655 3318 3982

13-6 143.14 1431 1718 2147 2863 3578 4294

14-0 153.94 1539 1847 2309 3079 3848 4618

14-6 165.13 1651 1982 2477 3303 4128 4954

15-0 176.71 1767 2121 2651 3534 4418 5301

15-6 188.69 1887 2264 2830 3774 4717 5661

16-0 201.06 2011 2413 3016 4021 5027 6032

16-6 213.82 2138 2566 3207 4276 5346 6415

17-0 226.98 2270 2724 3405 4540 5675 6809

17-6 240.53 2405 2886 3608 4811 6013 7216

18-0 254.47 2545 3054 3817 5089 6362 7634

18-6 268.80 2688 3226 4032 5376 6720 8064

19-0 283.53 2835 3402 4253 5671 7088 8506

19-6 298.65 2986 3584 4480 5973 7466 8959

20-0 314.16 3142 3770 4712 6283 7854 9425

20-6 330.06 3301 3961 4951 6601 8252 9902

21-0 346.36 3464 4156 5195 6927 8659 10391

**As permitted by statutory building code or established by accepted tests.




Fig. 9.8 Reinforcement Details for a Grade Beam-drilled Pier Joint.

Fig. 9.9 Option 1 – Extend Column Dowels Straight Into the Drilled Pier.

Fig. 9.10 Option 2 – Provide a Deeper Grade Beam.

9.5 Grade BeamsWhen designing grade beams, it is commonly assumed that the soil beneath the grade beam is nonexistent and that support occurs at its ends only. Therefore, the design and detailing requirements and guidelines given in Chapter 5 of this Guide are applicable.

A unique challenge with grade beams occurs at the grade beam-drilled pier joint. If a grade beam is too shallow, conges-tion problems can occur at the joints (Reference 23). Consider the detail depicted in Fig. 9.8. Because the depth of the grade beam is relatively shallow, the longitudinal bars from the column and the dowel bars from the drilled pier need to be hooked to achieve proper development. Even with ideal bar placement, it would be very difficult to properly fit all of the bars. This congestion problem would be compounded if the bars from the members were larger or if there were an intersecting grade beam at the joint. Six options to alleviate this problem are examined below.

Option 1 – Extend the column dowels straight into

the drilled pier

Extending the column dowel bars straight into the drilled pier alleviates some of the congestion problems (see Fig. 9.9) However, there are some issues associated with this detail:

• Special coordination would be required where the contractor for the drilled pier is different than the contractor for the remainder of the structure. The drilled pier contractor may not be permitted to install the column dowels so this would require coordination at a time when the building contractor may not be on site yet.




Fig. 9.11 Option 3 – Provide a Deeper Grade Beam only at the Drilled Pier.

Fig. 9.12 Option 4 – Provide a Pile Cap Under the Grade Beam at the Drilled Pier.

Fig. 9.13 Option 5 – Hold Back the Concrete from the Pile Top. Fig. 9.14 Option 6 – Place a Blockout at the Top of the Drilled Pier.




Fig. 9.15 Transverse Reinforcement of Special Boundary Elements at Foundations.

• Column dowels that are cast into the drilled pier cannot be moved or adjusted to accommodate grade beam rein-forcement or column locations.

• For drilled piers with large diameters, the tolerance on pier location is much larger than that for the column it is supporting. Thus, if column dowels are installed in the drilled pier in accordance with the drilled pier tolerances, they may be positioned away from the intended locations. In such cases, it is not clear which contractor would be responsible to correct this problem.

Option 2 – Provide a deeper grade beam

Providing a deeper grade beam may eliminate the need to provide hooks at the ends of the longitudinal reinforcement from the drilled pier thereby reducing congestion in the joint (see Fig. 9.10). The volume of concrete is increased in this option, but the amount of longitudinal reinforcement in the grade beam may be reduced because of the larger effective depth for flexure.

Option 3 – Provide a deeper grade beam only at the

drilled pier

Deepening the grade beam at the location of the drilled pier only would be a viable option similar to Option 2 (see Fig. 9.11). The thickened section would be cast with the grade beam. A smaller volume of concrete would be required com-pared to Option 2, and there would be a negligible difference in the required amount of longitudinal reinforcement in the grade beam.

Option 4 – Add a pile cap under the grade beam at

the drilled pier

Adding a pile cap beneath the grade beam at the location of the drilled pier also alleviates congestion issues (see Fig. 9.12). This pile cap would likely be cast separate of the grade beam.

Option 5 – Hold back the concrete from the pile top

Where a grade beam is supported by a concrete-filled steel pile or casing, a viable option to alleviate congestion is to fill the steel jacket with concrete to an elevation that is sufficiently below the top of the jacket so that the column dowels can project into the pile with the proper embedment length (see Fig. 9.13). This option is similar to Option 1 except that in this option, the column dowels are placed with the grade beam; this allows a certain amount of adjust-ment in placing the dowels. The top of the pile is subsequently filled with concrete when the concrete for the grade beam is cast.

Option 6 – Place a blockout at the top of the drilled pier

This option is similar to Option 5 (see Fig. 9.14). The blockout is filled when the concrete for the grade beam is cast.


9.6.1 Overview

Design and detailing requirements for foundation elements supporting structures assigned to SDC D, E, or F are given in ACI 18.13. Specific requirements and guidelines for the foun-dation types covered in the previous sections of this chapter are summarized below. All of the requirements and guidelines presented above are also applicable.

9.6.2 Footings and Foundation Mats

Longitudinal reinforcement of columns and structural walls that are part of the SFRS of a structure must be fully devel-oped for tension in a footing or mat foundation. Standard hooks can be utilized at the ends of the bars where the foun-dation element is not deep enough to accommodate straight bars, but providing straight bars is recommended.




Fig. 9.16 Requirements for Footings and Foundation Mats in Structures Assigned to SDC C, D, or F.

Fig. 9.17 Requirements for Grade Beams in Structures Assigned to SDC C, D, or F.

The transverse reinforcement of columns or boundary ele-ments of special structural walls must extend at least 12 in. into the supporting footing or mat provided the edge of the column or wall is located greater than one-half the foundation depth from the edge of the foundation (ACI 18.13.2.3). For columns or boundary elements located closer than that, the transverse reinforcement must extend a length equal to the development length of the longitudinal reinforcement in the column or boundary element (see Fig. 9.15 for the case of a special boundary element, which is adapted from Reference 7). The intent is to prevent an edge failure of the foundation element. Additional reinforcement details can be found in Fig. 9.16, which is adapted from Reference 7.

9.6.3 Grade Beams

Cross-section limitations and closed tie requirements of ACI

18.13.3 for grade beams are summarized in Fig. 9.17, which is adapted from Reference 7. For grade beams that are part of a mat foundation that resists flexural stresses from columns that are part of the SFRS, the detailing requirements of ACI 18.6 for beams of special moment frames govern.

9.6.4 Piles, Piers, and Caissons

The design and detailing requirements for concrete piles, piers, and caissons in ACI 18.13.4 are given in Fig. 9.18, which is adapted from Reference 7. These provisions, as well as those in ACI R1.4.6, helps to ensure that these foundation ele-ments perform as intended during a design seismic event.




Fig. 9.18 Requirements for Piles, Piers, and Caissons in Structures Assigned to SDC C, D, or F.




CHAPTER 10 References1. American Concrete Institute (ACI), Committee 318. 2014.

Building Code Requirements for Structural Concrete and Commentary, ACI 318-14, Farmington Hills, MI.

2. Concrete Reinforcing Steel Institute (CRSI). 2015. Reinforcing Bar Detailing, 5th Edition, Schaumburg, IL.

3. Concrete Reinforcing Steel Institute (CRSI). 2009. Manual of Standard Practice, Schaumburg, IL.

4. Concrete Reinforcing Steel Institute (CRSI). 2014. Design Guide for Voided Concrete Slabs, Schaumburg, IL.

5. R.S. Means Co., Inc. 2015. Concrete and Masonry Cost Data, Rockland, MA.

6. American Concrete Institute (ACI). Concrete Cover at Rustications, Drip Grooves, and Formliners, Concrete International, June 2010, pp. 35-38.

7. Fanella, D. A. 2015. Reinforced Concrete Structures – Analysis and Design, 2nd Ed., McGraw-Hill, New York, NY.

8. American Concrete Institute (ACI). Reinforcing Bar Layout for Two-way Slabs, Concrete International, November 2012, pp. 37-40.

9. American Concrete Institute (ACI). Layering Reinforcing Bars, Concrete International, January 2010, pp. 53-56.

10. Birley, D. Beam-Column Joints, Concrete International, December 2006, pp. 45-47.

11. American Concrete Institute (ACI). Wide Beam Stirrup Configurations, Concrete International, March 2010, pp. 62-64.

12. American Concrete Institute (ACI). Steps in Beams, Concrete International, June 2012, pp. 41-44.

13. American Concrete Institute (ACI). 2009. ACI Design Handbook, SP-17(09), Farmington Hills, MI.

14. Concrete Reinforcing Steel Institute (CRSI). 2011. CRSI Design Handbook, 11th Ed., Schaumburg, IL.

15. American Concrete Institute (ACI). Detailing Concrete Columns, Concrete International, August 2011, pp. 47-53.

16. American Concrete Institute (ACI). Column Tie Configura-tions, Concrete International, March 2013, pp. 45-50.

17. American Concrete Institute (ACI). Column and Boundary Element Dowels, Concrete International, December 2012, pp. 44-48.

18. American Concrete Institute (ACI). Bar Detailing at Wall Openings, Concrete International, December 2010, pp. 52-56.

19. American Concrete Institute (ACI). Corner Details for Wall Horizontal Bars, Concrete International, September 2009, pp. 43-45.

20. American Concrete Institute (ACI). Location of Vertical Bars at Wall Intersections and RFI 12-02, Concrete International, August 2012, pp. 47-51.

21. Concrete Reinforcing Steel Institute (CRSI). 2014. Design Guide for Square Spread Footings for Individual Columns, Schaumburg, IL.

22. American Concrete Institute (ACI). Reinforcing Bar Details for Mat Foundations, Concrete International, February 2012, pp. 48-52.

23. American Concrete Institute (ACI). Grade Beam Depth and Dowel Embedment, Concrete International, May 2009, pp. 53-56.

24. American Concrete Institute (ACI), Committee 237. Self-Consolidating Concrete, ACI 237R-07, Farmington Hills, MI.

25. International Code Council (ICC). 2015 International Building Code, Washington, D.C.




NotationsA = tributary column area, in.2

Abs = cross-sectional area of spiral reinforcement, in.2

Ach = cross-sectional area of a member measured to the outside edges of transverse reinforcement, in.2

Acp = area enclosed by outside perimeter of concrete cross section, in.2

Acv

= gross area of concrete section bounded by web thickness and length of section in the direction of shear force considered in the case of walls, and gross area of concrete section in the case of diaphragms, not to exceed the thickness times the width of the diaphragm, in.2

Af = required area of footing

Ag= gross area of concrete section, in.2 For a hollow section, Ag is the area of the concrete only and does not include

the area of the void(s)

Ash= total cross-sectional area of transverse reinforcement, including crossties, within spacing s and perpendicular to

dimension bc, in.2

As,min = minimum area of flexural reinforcement, in.2

Ast= total area of nonprestressed longitudinal reinforcement including bars or steel shapes, and excluding prestressing

reinforcement, in.2

b = width of compression face of member, in.

bc= cross-sectional dimension of member core measured to the outside edges of the transverse reinforcement

composing area Ash, in.

bt = width of that part of cross section containing the closed stirrups resisting torsion, in.

bw = web width or diameter of circular section, in.

Bn = nominal bearing strength, lb

Bu = factored bearing load, lb

c = distance from extreme compression fiber to neutral axis, in.

= distance from face of column to edge of footing, ft

cc = clear cover of reinforcement, in.

cs = clear concrete cover to stirrups, in.

c1= dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction of the

span for which moments are being determined, in.

c2= dimension of rectangular or equivalent rectangular column, capital, or bracket measured in the direction

perpendicular to c1, in.

d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.

dagg = nominal maximum size of coarse aggregate, in.

db = nominal diameter of bar, wire, or prestressing strand, in.

dbell = bell diameter of a drilled pier

dshaft = shaft diameter of a drilled pier

N-1Concrete Reinforcing Steel Institute



ds = diameter of stirrup reinforcement, in.

Dch = diameter of the column core measured to the outside edges of the spiral reinforcement, in.

E = effect of horizontal and vertical earthquake-induced forces

f 'c = specified compressive strength of concrete, psi

fs = tensile stress in reinforcement at service loads, excluding prestressing reinforcement, psi

fy = specified yield strength for nonprestressed reinforcement, psi

fyt = specified yield strength of transverse reinforcement, psi

h = overall thickness, height, or depth of member, in.

h1 = depth of drop panel, in.

hw = height of entire wall from base to top, or clear height of wall segment or wall pier considered, in.

hx= maximum center-to-center spacing of longitudinal bars laterally supported by corners of crossties or hoop legs

around the perimeter of the column, in.

k = effective length factor for compression members

kf = concrete strength factor

L = length of footing or drop panel measured in the direction of analysis

ℓ = span length of beam or one-way slab; clear projection of cantilever, in.

ℓc = length of compression member, measured center-to-center of the joints, in.

ℓd= development length in tension of deformed bar, deformed wire, plain and deformed welded wire reinforcement,

or pretensioned strand, in.

ℓdc = development length in compression of deformed bars and deformed wire, in.

ℓn = length of clear span measured face-to-face of supports, in.

ℓo= length, measured from joint face along axis of member, over which special transverse reinforcement must be

provided, in.

ℓw = length of entire wall, or length of wall segment or wall pier considered in direction of shear force, in.

Mn = nominal flexural strength at section, in.-lb

Mpr

= probable flexural strength of members, with or without axial load, determined using the properties of the member at joint faces assuming a tensile stress in the longitudinal bars of at least 1.25fy and a strength reduction factor of 1.0, in.-lb

Mu = factored moment at section, in.-lb

n = number of items, such as, bars, wires, monostrand anchorage devices, anchors, or shearhead arms

nmax = maximum number of longitudinal reinforcing bars that can fit in a single layer

nmin = minimum number of longitudinal reinforcing bars required in a single layer

P = total service axial dead and live load on a drilled pier

ph = perimeter of centerline of outermost closed transverse torsional reinforcement, in.

Pn = nominal axial compressive strength of member, lb

N-2 Concrete Reinforcing Steel Institute



Pn,max = maximum nominal axial compressive strength of a member, lb

Po = nominal axial strength at zero eccentricity, lb

Pu = factored axial force; to be taken as positive for compression and negative for tension, lb

qa = allowable bearing capacity of the soil or rock, lb/ft2

qu = factored load per unit area, lb/ft2

r = bend radius of a reinforcing bar

Rn = nominal strength coefficient of resistance

s = center-to-center spacing of items, such as longitudinal reinforcement, transverse reinforcement, tendons, or anchors, in.

so = center-to-center spacing of transverse reinforcement within the length ℓo, in.

Vc = nominal shear strength provided by concrete, lb

Vu = factored shear force at section, lb

W = length of drop panel measured in the direction perpendicular to L

f= ratio of flexural stiffness of beam section to flexural stiffness of a width of slab bounded laterally by centerlines

of adjacent panels, if any, on each side of the beam

= ratio of long to short dimensions: clear spans for two-way slabs, sides of column, concentrated load or reaction area; or sides of a footing

= modification factor to reflect the reduced mechanical properties of lightweight concrete relative to normal weight concrete of the same compressive strength

= ratio of As to bd

ℓ = ratio of area of distributed longitudinal reinforcement to gross concrete area perpendicular to that reinforcement

s= ratio of volume of spiral reinforcement to total volume of core confined by the spiral, measured out-to-out of

spirals

t = ratio of area of distributed transverse reinforcement to gross concrete area perpendicular to that reinforcement

= strength reduction factor

Ωo= amplification factor to account for overstrength of the seismic-force-resisting system determined in accordance

with the general building code

N-3Concrete Reinforcing Steel Institute



Notes

Concrete Reinforcing Steel Institute



Concrete ReinforcingSteel Institute

933 North Plum Grove Road Schaumburg, IL 60173 Tel. 847.517.1200 www.crsi.org

Description of ManualThe purpose of this guide is to present information on how to

select economical reinforced concrete floor systems and to present

requirements and guidelines on how to size, design, and detail

reinforced concrete structural members that, where implemented,

will result in economical reinforced concrete structures.

10-DG-STRUCTURES-2016-2m

9612077819439

ISBN 9781943961207


crsi-design guide for economical reinforced concrete

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